Wild Shape is pretty important to Moon Druid.

I'm currently playing a Moon Druid, and Wild Shape is key to the effectiveness of a Moon Druid in combat. If your players had wanted a spellslinger Druid, Circle of the Moon was not a great choice. Circle of the Land or another Circle that improves spellcasting would be a much better choice.

TL;DR: Yes, as a Circle of the Moon Druid they should definitely be focusing on their Wild Shapes if they want to be most effective in combat. However, you can play the character and have fun without Wild Shaping in combat by slinging spells (particularly healing and control spells such as Cure Wounds, Healing Word, Entangle, Faerie Fire, etc).

Your best course of action depends on why they aren't using the Wild Shape. Are they making the conscious decision not to, whether for story or personal reasons, or are they just not using it because they're inexperienced and not sure how to use it properly? Or, perhaps they aren't using Wild Shape in combat because they see the party composition and they don't want the entire party to be in the front line swinging at the enemy, so they choose to hang back instead.

Now, if they're complaining about their characters' low HP, then I would hazard a guess that it's because they're inexperienced and don't know any better. In that case, I'd pull them aside together (with the DM if possible) between sessions and show them some of the cool shapes they have access to (not sure what level you guys are but Giant Hyena, Dire Wolf, Giant Toad, and Giant Spider take the cake at low levels for me).

Yes, you probably have seen a Brown Bear, Lion, Tiger or Dire Wolf at some point.

If they insist that they haven't seen any of those beasts yet, you'll have to talk them through the process of going through their characters' lives BEFORE they became adventurers and consider what they would have seen during that time. Page 24 of Xanathar's Guide to Everything has a really good bunch of tables on it that they should have a look at. The tables are organized by biome (grassland, forests, mountains, etc) and have a fairly long list of beasts up to CR 1 that your characters would have probably seen during their lives pre-adventuring if they were from that type of area.

Discuss with your DM and those two players and see what you can work out. If you have noticed their complaining and lack of Wild Shapes, the DM probably has as well. If you include your DM in the process it'll go much smoother.

Inspiration/Excitement for your players

--Warning: D&D Math Below!!!---

My MVP wild shape pre-level 4 for prolonged combat has got to be Giant Hyena. I'm going into power-gamer mode for a minute here: doing some basic math, 45HP per wild shape (giant hyena) at 2 transformations per rest is 90HP. If we assume level 3 then you have 4 first level spell slots and 2 second level spell slots, for a total healing amount of 8d8 hit points over the course of 6 turns (one slot per turn), which averages 36 hit points. If you assume that your characters have 12 CON (+1 bonus) and that they take average HP at each level up, they will have 19HP at level 3 on the un-transformed character itself.

Adding this all up, you have 90HP + 36HP + 19HP which is 145HP at level 3, assuming average healing and HP rolls and that you expend all of your resources, and that's without any external assistance such as your cleric or health potions. Show that to your Druid players and hopefully they stop complaining about low HP.

Conclusion

I don't mean to encourage extreme powergaming and it's unrealistic that they would blow all of their spell slots on healing and all their wild shapes in a single combat. I mainly wanted to show how effective the Wild Shapes can make the Moon Druid and hopefully this can inspire and excite your players to get into the next game and try out their Wild Shapes, instead of hanging back and slinging Thornwhips and Ice Knives.

Combat-wise, it feels a bit much.

I recently started a druid. My first intent was to find a way to remain effective in combat despite depleted resources ; I found out that the druid hasn't much to offer, in that regard:

1. Ranged options (such as sling attacks, or produce flame) lack range and damage.
2. Melee options (such as shillelagh or thorn whip) lack damage in the long run.
3. AC is often on the low-end - unless your DM is generous on non-metal armor distribution, or you focus on dexterity.

It is indeed very frustrating, and encourages battlefield control over direct damage. Your homebrew subclass fixes all 3 issues, including strong blaster, healer and tank features: it would have been a no-brainer for me, and that's a warning for balance.

Bladesinger comparison

There are not that many full spellcasters with Extra Attack, and Bladesong looks very close to Heart of Fire. It may seem balanced... until you dig a little more:

\$\begin{array}{|c|c|c|} \hline \textbf{Ability} & \textbf{Bladesinger} & \textbf{Circle of flame}\\ \hline \text{max AC using mundane gear} & 23 & \textbf{25} \\ \text{Requirements:} & \textit{mage armor}\text{ spell} & \text{shield, class level 18} \\ & \text{high dexterity & intelligence} & \text{high dexterity or nonmetal half-plate} \\ \hline \text{max AC using magical items} & 25 & \textbf{31} \\ \text{Requirements:} & \textit{robe of the archmagi} & \text{+3 shield & armor, class level 18} \\ & \text{high Dexterity & Intelligence} & \text{high Dexterity or nonmetal half-plate} \\ \hline \text{Hit dice} & \text{d6} & \textbf{d8} \\ \hline \text{Damage control} & \text{reaction & spell slots-based} & \textbf{healing spells} \\ & \text{Damage reduction} & \textbf{reaction-based healing} \\ \hline \text{Concentration}& \text{+Intelligence modifier} & \text{better AC = fewer concentration checks} \\ \hline \end{array} \$

All in all, the Circle of the Flame druid vastly outperforms its cousin - and can even do so with little ASI investment, should you find a proper armor.

Circle of Land & Circle of Spores comparisons

The Circle of Spores, from Unearthed Arcana, is probably an attempt to offer wannabe-melee druids an alternate to the circle of the moon's combat forms. Let's include it here:

\$\begin{array}{|c|c|c|} \hline \textbf{Subclass features} & \textbf{Circle of the Flame} & \textbf{Circle of the Land} & \textbf{Circle of Spores} \\ \hline \text{level 2} & \textbf{$fire\ bolt$} & \text{one druid cantrip} & \textit{chill touch} \\ & \textbf{1-minute huge melee buff} & \text{Natural Recovery} & \text{10-min small melee buff} \\ & & & \text{reaction-based poison damage} \\ \hline \text{level 6} & \textbf{Extra Attack} & \text{ignoring difficult terrain} & \text{1-hp zombies} \\ \hline \text{level 10} & \textbf{+Wis mod to fire, concentration spells} & \text{various immunities} & \text{AoE spores} \\ & \textbf{fire resistance} & & \\ \hline \text{level 14} & \textbf{turn fire/lightning damage into healing} & \text{beasts & plants hesitate to attack} & \text{various immunities} \\ \hline \end{array} \$

It looks like the Circle of the Flame has the best features at each level: best cantrip to allow ranged combat, best melee-buff, extra attack is sick, enhancing concentration-based spells is unique... Even the last feature, that appears situational at first, becomes cheesy once you start to fuel it with your own AoE spells.

Suggestions

So, how do we fix this?

First, you can't aim for balance, and be a strong healer, blaster and tank at the same time. I removed the healing capabilities, as the tank part seemed your main concern, and the theme calls for improved fire damage.

Second, on the AC question: "no metal armor" and bounded accuracy make things difficult. If your DM rewards you with powerful nonmetal armors, he shouldn't allow big AC temporary bonuses in an homebrew class. The opposite is also true: if he allows big AC temporary bonuses... he should make sure you keep a lowly hide armor for your entire career. Hence the solution offered here - which seems the good way to reliably get good AC, without over-investing in dexterity or "forcing the hand" of your DM.

Here's the result:

Only You

When you choose the Circle of Flame at level 2, fire bolt and green-flame blade become druid cantrips for you. You learn an additional druid cantrip of your choice.

Leaves choices, and includes another fire-themed cantrip. Green-flame blade is mostly aimed at tier 2+ melee: extra attack was too much (especially if you intend to add Polearm Master), but this cantrip offers something comparable to the cleric's Divine Strike.

Heart of the Flame

At 2nd level, you gain the ability to awaken the primal spirits of flame. As a bonus action, you can expend a use of your Wild Shape feature to awaken your inner flame, rather than transforming into a beast form. While this feature is active, you gain the following benefits:

• You gain 3 temporary hit points per level you have in this class
• You shed bright light in a 30-foot radius and dim light for an additional 30 feet.
• You add your Wisdom modifier to concentration checks.

These benefits last for 10 minutes, or until you become unconscious.

Temporary HP is probably the way to go to add survivability to a druid: it matches what has been done for the Circle of Spores and Circle of the Moon. I removed the AC boost: if you insist on keeping it, you'll have to either keep it low (like +2), or remove the ability to use a shield - if you care about bounded accuracy, of course.

Purification through Fire

Starting at level 6, you gain resistance to fire damage. You also learn a purification ritual that allows you to prepare metal shields & armors, so that you can use them.

With your average 14-dex druid, it means up to +3 AC - and an easier access to magic armor in the long run. It is a game changer for most tables, where nonmetal armor is scarce - and can be balanced by making the ritual as simple or as complex as you wish (involving time, gold, crafting skills, a risk to destroy the item?).

Heat of Battle

Starting at level 10, once per turn, whenever one of your spells inflicts fire damage to a creature, you can add your Wisdom modifier to that damage.

Idea is to open that damage buff to more options (e.g fire bolt, green-flame blade) - while keeping it at a reasonable level (only one creature per turn).

Flaming Soul

Starting at level 14, you gain immunity to fire damage. You can also apply your heat of battle on a second damage roll, each turn.

Either affect both targets of green-flame blade, or use it on both flaming sphere and your cantrip of choice.

I'm absolutely not sure that this is well balanced:

• I feel Nature and/or Forge Domain clerics might feel cheated with this, as some of their core subclass features are included here, with few drawbacks
• having both a better AC and temporary HP, while keeping access to healing spells, means that you are tanking pretty hard
• Extra attack was too much - and this may also be. Green-flame blade + Heat of Battle + shillelagh makes a strong combination.
• Bonus to concentration might go out of control if you go for the War Caster / Resilient (Con) route. Replacing it with Con save proficiency or advantage on concentration checks may help avoid those shenanigans.

But I do think it is closer to "balanced", when compared with Land & Spores druids. Obviously, feel free to switch things around (access to metal armor as soon as level 2?) - and take or leave whatever fits best your idea.