Do I have a right to complain that my X lets his girlfriend spend the night when the kids are there?

you could complain but I doubt anything will change, he's not going to tell you to not have men over when the kids are at your house

No. It is his home unless she is a known criminal and you can prove she poses a danger I would leave this one alone. You don't want him coming in and dictating what you do at your home leave him alone at his house.

You can complain all you want but you nor a judge will stop it. You can't dictate who he takes the kids around or let's spend the night at his house unless they're a child molester, etc

yes cause they can be banging in front of them;]

You have the right but the way the law works they won't really do anything about it:/

No, you have to realize you can't control everything. It is his house and unless there is a danger to the kids, you don't have any say in it.

Unless she's harming your kids in some way..I don't think so.

In my brother's divorce, the court papers stipulated that there could be no overnight guests of the opposite sex (his wife didn't care about that), but he never pushed the issue on her end but he did make sure his girlfriend never spent the night when he had the kids.
You can include it, or have it put it court papers but I'm not sure how you'd go about proving it was happening or what his penalty would be other than violation of court order.
Personally I think it's wrong to do that with the kids in the house, but that's only my opinon. It seems to me like both parents would want their kids to not think so casually of sex, love and relationships. It's just a bad example to me and I'm not talking about people in long term relationships where the kids don't even realize they're not married, but the one's that get new mates on a regular basis.

I wish we could've done something about my stepsons' mother whoring it up with a new boyfriend every 3 months in her singlewide, but no. You can only control your own household, not the other.