Re: So she is in a fix now.
I think it is imperative for her to focus on her life with her husband. My brother told me soon after my nikah that the most important male in my life is essentially my husband now and I should consider his wants and needs before all else's.
This is not to say that my father or brothers are not important now. My brother is younger than me by a few years, but there is a lot of wisdom in what he said. What I feel in this situation is that she should not spend time overnight at her parents' home for the time being. Even if it is just for one day or two in a week. She can go there when the husband is at work or in between, but the point is that it should not at this time infringe on their time together, or whatever time they do get together.
It really is not a matter of her family or his in my opinion, and who is doing how much for whose parents. It's more about the couple. His family is conveniently right there, at home. And she can attend to them nicely, being the person you have described her to be. Her family is not so conveniently present right there. Think of it as her visiting some random person's house on a weekly basis early in the marriage. Perhaps and most likely he wants them to focus on a life together, on building one and establishing strong bonds together, which btw is a BIG blessing. It is marvellous and it is something to be thankful for that the boy is possessive of her and wants perhaps to work on THEIR life together. There are cases where girls don't get that and the boy couldn't care less if she was there or not.
Successful marriages I've seen, including the older lot of my parents' friends, I have observed that the woman always puts the husband first and is there to greet them every day when they get home and basically make them feel like kings. Husbands, usually less expressive, acutely feel their wives absence and though are appreciative of them when they are around, it is not expressed in so many words. Except in the displeasure when they aren't there.
That is my very humble opinion, that for the betterment of her marriage, which is her life from hereonin, she should make sure that her visits do not infringe upon her husband and her potential alone time, whenever that may be. She can increase phone calls but I would discourage her from attending any call from anyone when she and her husband are together. It shows how much importance you give the other person, and again in my opinion, men like to know they are important just as much as females do. Whenever my husband and I are together, if my phone rings and it's a friend, I almost always let it go unanswered or only have a very short conversation in which i relay that I am busy right now with the husband and I shall get back to the friend. If it is his family or mine, I shall take the call, relay that I am with him and listen to what they have to say because that is giving them respect as elders. My family members usually understand and give me space. His are fine because if the conversation goes longer, I offer him the phone so that he is involved.