Children sometimes view a divorce as a way to manipulate parents into giving them their own way. The issue here is that they might claim that one parent already approved an activity or that they get to do specific things at the other parent's house. By making these claims, they are hoping that they will get to do what they want.
As a newly single parent, it is up to you to set the rules for your house. You need to think about how you want things to work. Once you set the rules, relay them to the children, and don't deviate from them.
If you say no eating in the bedrooms, you might have a child who comes back to you saying that the other parent said eating in the bedroom is acceptable. This is when you need to put your foot down and remind them that you are the adult in the home.
Some parents find it easier if they work with their ex to come up with major rules that span both homes. When both parents are on the same page about things like a teen's curfew, the confusion is usually minimized. This also takes away some of the temptation to play one adult against the other.
It isn't going to be easy for the children to adjust to the different rules in two different homes after a divorce. You should be firm yet understanding about efforts to push the limit or manipulate you. Sometimes, just giving the child a warning about following the house rules might be all it takes to help them with the adjustment.
You should be sure that you have a detailed custody order that outlines what each parent is responsible for. This can help you if issues come up. Having the biggest rules and expectations outlined in writing can make parenting with your ex a simpler matter.