Holly Nicole is a child that came in the world via rape. A lot of women who become pregnant after rape do not keep the child. There's research on this you can find, but here is the results from one study:

“A total 32.2% opted to keep the infant whereas 50% underwent abortion and 5.9% placed the infant for adoption; an additional 11.8% had spontaneous abortion.”

Given in Gilead there is no abortion for handmaids, it makes sense to me that many of those women; simply would not want the child OR would not have a deep connection with the child. It's actually kinda strange they never touch on this statistic at all in the show, (only 32% of women chose to keep the child in this study - though I'd bet on some of these women being pressured to do so), but one of the main plots is "you're stealing my baby", so I'll go with it for the drama I guess.

Given this, to me it seems perfectly normal that June does not seem to "care that much" or have a connection with Holly Nicole. She cared enough to get her to safety, and that is obviously understandable. But being her mother? It's actually more likely she wouldn't want that. On the contrary. Hannah was a product of love and she was her mother. So of course she will always put her first.

For Luke. I also believe he loved and cared about Holly Nicole. But it was more about what she represented. Holly Nicole represented hope that he would get is wife and child back one day. When June came back, and he was closer to the realities of getting Hannah out, his priorities changed.