One of the most frustrating things about being a single parent is how to deal with two sets of rules the children face. It is tempting to think that there is a right way and a wrong way and your way is best. This approach can cause a lot of conflict and stress. However, there are lots of ways to parent and keeping that idea in mind will help you deal with the differences between you and your ex's parenting style.

First, are you clear on the rules you have for your home? It would be good to have a family discussion with your children. Let them say what they think would be good rules to have. Set consequences for when the rules are broken. Post them where everyone can see them.

Then you can state that these are the rules for this house and you expect them to be followed.

The children will be more willing to follow the rules if they get to help create them. And when you have to follow through on a consequence, you can point to the posting and say, this is what we agreed on, it will make you less of a bad guy.
Now that you are clear on what you want, you can stand firm when you hear,
"But I get to do it at Dad's (Mom's) house."
You can reply "Well, that's allowed at the other parent's house but it's not here. "
Again, you can point to the posted list.

Realize that sometimes the child will tell you it is allowed someplace else to get you to change your mind. This may not be a complete fact. Also understand that two parent families have to deal with different parenting styles.

Decide to respect the other parent's rules. You would want them to do the same for you. You don't have to agree or like the rules but then the same can be said for some of the rules at your child's friend's houses as well.

If you are clear on what you expect in your home, and you can respect the other parent's choices, this issue will become a non-issue. And as you do this, it will relieve tension that can arise from conflict.
Don't allow the fact that your child has two sets of rules to upset your household. Model for your children how to respect differences of opinions while standing up for their own.