My point is that "gets to be" has a positive connotation that the thing is desired, and a weaker connotation that one is free to decline.

"You get to be the first customer at the ice cream shop!" does not imply that you are required to be the first customer: it is yours to accept if you wish, but you may decline.

So if you wanted to highlight an unfair aspect of people's expectations, you ought to choose different phrasing.

For bonus points, since women do have an advantage in custody battles, and parents generally do want to be around their children, if you argue that expectations are unfair in some way it would also be good to argue that this isn't just the payment one has to make for a greater privilege.

For instance, if I complain that receiving a large inheritance means I have to spend more time with accountants and tax preparers, you quite reasonably might still view that I am in an enviable situation compared to people who don't receive the inheritance. (For instance, you you and I were siblings and I got the entire inheritance, you probably wouldn't think it justified that I was complaining about how much time I had to devote to investment planning.)

But even if you don't go for the more comprehensive discussion--you were just listing bullet points after all--the language you used phrases the situation as a privilege, not a burden.