I'm a stepmom to 2 girls, and my husband's ex was very jealous and insecure.
I would recommend that you be a little less effusive in showering the girls with too much - the extra room is fine, but go easy on the car. If Mom is trying to discipline them and you come off as the party person always giving them extras, it undermines her even though you don't mean to do so. If she grounds them for not doing their homework, and you reward them with a car (without knowing they are grounded), then you are the bad guy.
If you are building a beautiful new house, Mom may be worried you are trying to lure the girls away from her. They can come ANYTIME, you say, but their mom has a right to weekends as well. So you cannot appear to be urging them to bail out on Mom's rules in order to find a retreat with you.
You must take the high road and not respond to the badmouthing. I don't know how you know what she says about you to the kids - but do not engage in conversations about that with them. Other people are pretty used to exes not liking the new wife, and they will ignore it if you show the world the person you are.
We stepmoms can be great people, but we can be guilty of trying to hard to make everyone happy. We need to let the parents be parents, no matter how badly they might be doing it!
You also need to be sure that your 2 kids don't think you are going overboard with the other 2.
The longer you are married, the more confident you will get in this. They will love you and come to you as adults if you honor their mother and don't worry about trying to please her or get her to like you. She probably never will. That doesn't mean she is right. It just means that's how it is.
She cannot keep you from talking to them when they are with you, but you should not be calling them at her home. Let your husband handle that. Make them feel welcome, but always show respect for their mother. Be the person you want them to see, but don't throw it in their faces about how wonderful you are. They will see it. You don't have to prove anything to them. Just make it an enjoyable weekend without appearing to spoil them too much.