Is the bard college of dance homebrew balanced

Mostly balanced except for Dance of the Dead

Overall this subclass doesn't appear to be too unbalanced. Playtesting it as you are probably gives you a better idea than any of us would have purely from reading the rules.

Grim Secrets

Part one of this feature seems fine. Though no other college gain a cantrip at this level I don't feel this is fundamentally different to any of the others.

Part two is harder to guess at as it grants an ongoing improvement rather than a static benefit. To fully know if this is OP I would have to compare all necromancy spells to all bard spells and see if this adds a significant amount of power. I feel as though it may be a little over powered compared to the existing subclasses. Potentially consider moving this to the sixth level to mirror Additional Magical Secrets of the Lore Bard.

Haunted Eyes

Advantage against fear is common enough from many sources so not a big deal. Necrotic resistance is good but situational so not game breaking.

Dance of the Dead

This feature seems to be both over powered and goes against the normal design principles. For reference the other subclasses gain at this level:

• Additional Magical Secrets (Lore), two spells of your choice
• Extra Attack (Valor/Swords), as it says
• Mantle of Majesty (Glamour), Command as bonus action for 1 minute. Once per long rest
• Fool's Insight (Satire), detect thought CHA mod per long rest
• Mantle of Whispers (Whispers), situational disguise

This feature also uses Bardic Inspiration in a way that no other subclass uses them, more akin to the way superiority die are used than bardic inspiration.

This is the feature that needs the most work and I would consider scrapping entirely for something different.

Rule the still heart

This feature is fine, it could actually be considered weak since it only affects one creature per long rest and they get a saving (possibly with advantage).

Suggestions

This isn't too bad as a first attempt of the subclass. I would suggest re-doing dance of the dead. Potentially replacing it entirely. Allow me to propose some features for you, not sure if it suits 6th or 14th level better though.

Grave Humour

When an Undead Creature under your control, that you can see within 60 feet of you makes an attack roll, an ability check or saving throw, you can expend one of your uses of Bardic Inspiration, rolling a Bardic Inspiration die and adding the number rolled to the Undead's result. You must decide before the DM says whether the roll succeeds or fails.

Puppet Master - credit to Doc in comments

When you use the Attack action on your turn, if a creature you control can see you, it can use its reaction to make a melee attack. Only one creature you control can do this per round.

Good in Tier 1, underpowered in Tier 2+

No Heckling

This feature doubles the amount of disadvantage you can hand out on turns where you'd normally just cast a cantrip. It also allows you to make a weapon attack and still throw out vicious mockery. No Heckling is quite strong in Tier 1, but less interesting in Tier 2+:

• Monsters usually scale by adding more attacks (rather than a single big attack). This makes vicious mockery fall off in usefulness as Multiattack enters play.
• Weapon attacks from non-martial bards also fall off rapidly, often replaced by 1st or 2nd level spells (which prevent you from using No Heckling). At level 5, would you rather shoot a crossbow for around 6 damage, or force a Wisdom save for 10 + an opportunity attack from the barbarian (via dissonant whispers)?
• Bardic Inspiration competes for a bonus action, particularly at level 5+ when it recharges after a short rest.

Laughter is Contagious

Tasha's hideous laughter is a decent hard control spell for Tier 1 bards, mostly because it's the only generic one. Monster HP rapidly outpaces sleep. Hold person requires the same save for a much more lethal effect, but only works on humanoids. Suggestion has a ton of caveats and DM discretion.

Doubling the number of targets is a big boost to the spell's effectiveness, though the 5 foot requirement is highly restrictive. An upcast hold person requires that all targets be within 30 feet of each other and I frequently find that generous restriction too limiting.

And now for the elephant in the room: at level 5+, a twinned Tasha's hideous laughter needs to compete with fear and hypnotic pattern for concentration. This problem only gets worse as the number of spell slots increases. By level 9, the bard has seven spell slots of 3rd level or higher, many of which will be used for concentration spells.

Can't Stop Me

I just don't see this coming up very often. Even if it does (and you can't simply move out of the radius), hypnotic pattern is a fantastic spell that doesn't require verbal components.

You're Killing It

This shares shortcomings with Laughter is Contagious. You have to forgo hypnotic pattern and fear to use this, and I don't see it being worth the trade-off.

Tough Crowd

The first bullet point of this feature means Countercharm is actually usable! There are very few anti-charmed/frightened effects that protect an area. This won't come up every session, but when it does, it'll be extremely useful.

The second bullet point may have some out-of-combat issues. Countercharm has unlimited uses, so you could spam the Charisma save against a captured creature until it failed. The creature would then be indifferent until the bard got bored of using Countercharm. I would recommend granting a creature immunity for a minute (or an hour) on a successful saving throw.

Laughter is the Best Medicine

This seems fine. It's comparable to a Life cleric's Disciple of Life - lower level spells heal more than Disciple of Life; higher level spells heal less.

I'm on a Roll

Infectious Inspiration is a powerful (but balanced) feature for 14th level. This feature and Laughter is the Best Medicine certainly improve things, but the earlier features are rarely used at this level, leaving the subclass underpowered overall.

Potential fix for Laughter is Contagious

At higher levels, Tasha's hideous laughter must compete with fear, hypnotic pattern, and other fantastic spells for concentration. This is a critical balancing feature, preventing buff/debuff stacking. However, a single-target control spell with repeated saving throws might be weak enough to justify the following feature (replacing Laughter is Contagious):

When you use a spell slot to cast Tasha's hideous laughter, you can expend one use of your Bardic Inspiration to change its duration to 1 minute for this casting (no longer requiring concentration). When you do so, any other instance of Tasha's hideous laughter that you have cast using this feature ends.

This effectively allows you to target one creature with Tasha's hideous laughter without requiring concentration. You still get something like a twinned effect over the course of two turns, since you can cast the spell normally (with concentration) to target a second creature.

Anything that removes concentration should be watched closely for balance concerns, though I believe that this spell and feature have enough built-in caveats to keep things from getting out of hand.