Like most other answers, I would say yes, two shapeshifts in a combat is legit; no, you did not make a mistake by allowing your player to wolf out and; no, you shouldn't try to claw back the ability.
One thing I would add to the previous answers is that this issue will almost certainly balance itself out fairly soon. Yes, a CR 1 creature in a level 2 party is huge. But level 2 ends quickly.
At level 3, most classes get their archetype paths with cool powers and primary casters get level 2 spells. The wolf will be the same wolf it was before.
At level 4, a CR 1 creature is considered a medium encounter for a single party member. Everyone will be pumping their primary stat or taking a feat. Wolves don't get much out of Wisdom, nor is there much overlap between the feats that help them and those that work for druids.
At level 5, all classes see a major power spike. Cool abilities, level 3 spells, proficiency bonus goes up to +3. The party might also be finding minor, but interesting, magical items. While your Druid is kicking it lupine style, they won't get to enjoy any of that.
By level 6, the Druid can finally upgrade to a CR 2 creature! Of course, at 450 XP, a CR 2 is less than a medium difficulty solo encounter for a character that level.
The dire wolf will remain a CR 1 creature while the world around it scales up. On top of that, if your player wants to jump straight into wolf form every encounter, then every encounter is going to play exactly the same for them, because a wolf only gets the one basic attack.
I'd say, let your player have their fun. Everyone should get a chance to feel like they've beaten the system once in a while. It doesn't seem to be worth the trouble of taking that away from them if the whole situation will simply resolve itself in time.
I'd honestly be more worried that a character with a d8 hit die has 28 hitpoints at level 2.
Rule interpretation in general
There are two points to remember when looking at an ambiguous rule:
Your group, with the DM as final arbiter, decides the ruling for the rule. So, you need to establish what this is for each group that you play with.
Specific beats general. Start with the most general rule you can find and see how the specific rules change this.
Armor resizing in particular
For your issue, start with PHB p. 145 (ignoring the optional part because it makes no difference to the case at hand)
Variant: Equipment Sizes
In most campaigns, you can use or wear any equipment that you find on your adventures, within the bounds of common sense. For example, a burly half-orc won't fit in a halfling’s leather armor, and a gnome would be swallowed up in a
cloud giant’s elegant robe.
There's your general rule: no armor that fits a PC race (size S or M) would fit a bear (size L).
Wild Shape (p. 67 PHB) says:
Worn equipment functions as normal, but the DM decides whether it is practical for the new form to wear a piece of equipment, based on the creature’s shape and size. Your equipment doesn’t change size or shape to match the new form.
No help there; the armor will be too small and the wrong shape. In addition, there is a ruling that has to be made right here: is it practical for a bear to use armor even if it is the right size and shape? My ruling would be yes but your results may differ.
Now from DMG, p. 140:
In most cases, a magic item that's meant to be worn can fit a creature regardless of its size or build. Many magic garments are made to be easily adjustable, or they magically adjust themselves to the wearer.
The ruling needed here is does the hide armor a) need easy adjustment or b) magically adjust itself. If b) then all is easy, if a) then the druid may need to allow it to drop to the floor and then get some assistance to put it on which would take 5 minutes (PHB, p. 146) which makes it pretty useless in combat.
Those are the issues; your group needs to make the ruling.
Best Answer
A druid doesn't need a spellcasting focus to use Wild Shape.
A druidic focus is described as this:
The only thing a spellcasting focus does for any spellcaster is this:
You don't need a spellcasting focus to use any class features unless they say so, nor do you need a spellcasting focus to cast spells that don't have material components.
This means that a druid without any equipment can still cast many of their spells, and can use Wild Shape and any other class features.