That does sound like a very frustrating situation for you and your partner.
As I understand it, your problem is not so much that there are different rules at the two different homes. That's something you can talk with your ex about, but obviously you can't control it. And as you have discovered, kids do get used to the rules at each house being different and learn how to cope in each household.
The problem for you is that your girls have learned that the way to cope with rules they don't like at your house is just to leave at any time they want.
I love that your kids can make contact with their Dad at any time and visit whenever they want. But I don't think your setup is a good solution from the perspective of working things out with the parents at either home.
And I don't think this is just a problem for you. I think it is ultimately bad for your daughters. Kids do need the experience of sometimes running into limits and having to grieve about them. As long as we support them through that process, it builds resilience. I think what you're describing sets up a system where your girls don't get that experience.
So the obvious solution to me is that while your children should always have access to contact either parent, I would not let them simply exit either home when they don't like what's happening there. I would recommend a visitation schedule. Certainly your kids should have major say in that schedule, but once it is agreed-on by all parties, then changes and exceptions also have to be agreed on by all parties.
I know this is a big change. It will take the adults agreeing first, and then announcing it to the kids. You can expect some outrage. You'll need to listen carefully and accept their feelings about it. But ultimately, I think it will be much better for everyone. Good luck!