USAG safety regulations and often insurance would find a problem with the 18 kids scenario. I assumed the OP was in the US. Yes, there is a relatively small chance of something going wrong, but if it does your safety certification essentially says you were negligent. Most gyms will simply require the larger group pay a fee to cover the cost of a second instructor.
And as someone who fairly regularly does 18+ birthday parties and camps (with a second safety certified instructor), I would disagree that it's no big deal. You have an entire group of completely novice kids coming in, 60% are wearing completely inappropriate attire, some kids may be apprehensive about the gym for the first time, and they all have existing friendships so the potential for rowdiness is worse than a group of 18 random kids.
Just getting everything signed and everyone ready at the door is a nightmare, no matter how many times you told them the apparel policies, etc. Maybe people in other countries are better at following instructions, but here it seems there's no way to spell it out and have people do it.
Consequently, I find doing birthday parties very stressful, and only do it for kids I coach. The kids generally have a fantastic time but it's much harder than a normal class.