Okay, so I read an interview from the actress that plays Regina. She said she felt Regina does care for him and that she is more off put by Emma wanting to come back in his life.
I'm not sure if the show has done a good job of showing that, they do more to show that Henry doesn't trust her and showing how he is growing closer to Emma. No where have I seen, Regina do something that seemed like a mother would do.
Yes, she built a park, but out in the woods where any creepy person can just walk in a grab a kid? Seriously, that's the worst idea for a playground to be surrounded by trees in the woods.
She named him after her father, that's true. But still, I don't think the show let's us see that.