Birthday party etiquette

Ok I'm planning my 3 year olds 4th birthday and I'm a little unsure about something so I'd like some input!

We are only inviting the main group of people and by that I mean my parents and siblings and their kids, and same for my husband's side.

My one sister has started a whole bunch of drama with my family. We basically are just done with her crap. She is also dating this guy who I am not a fan of at all. I do not care for him because he's just a real POS. Anyways, he has 5 kids!! My sister has 3! I don't really plan on including him in the invite, just my sister and her kids but I know for a fact he will still come anyways. But I don't know if his kids will come, I'm not really sure about the situation he has with them. But they are such disrespectful kids, and I know its not their fault they are being raised that way. But they're kids I don't want around my kids. My son is already in that phase where he likes watching/playing with the "older" kids and he's starting to repeat them. His youngest daughter (2) bit my son (1) so hard at Easter that she drew blood and he had a bruise from it that has just now completely healed. My husband suggested that we just tell my sister that we will cover the charge for her and her kids but he will have to cover his charge and the charge for his kids. Which is $5 each and maybe they just won't show up. They'll also have to drive an hour and they probably couldn't afford the gas for it anyways.

My husband also suggested that we just don't invite her all together since we don't have a good relationship anyways. But I feel like that's more rude.

So I really don't know what to do.