Cate and Tyler seem pretty clueless about parenting and what it takes. And sending Nova to Cate's mom's house 2-3 nights per week is a pretty outrageous decision for two non-working parents to make (especially given Cate's mom's history). Clearly Cate has some issues going on (i.e., depression, guilt, etc) and she should be engaging in some intense counseling.
That being said, I think that Tyler's mom seemed somewhat jealous/resentful that Nova was always at Cate's mom's and not available when she was able to make it to visit. She works, right? And has a life that involves typical adult responsibilities? So she is probably not able to keep Nova nearly as much as all of these unemployed people.
I loved how she gave Tyler the business about being lazy.