Re: One more thing... I think she was just pushing her to develop parts of herself that were important and that she really did need.
Exactly. And that's what makes Babs more the active parent, and why it would make more sense for Babs to offer to adopt Cass, rather than Bruce.
it sort of reminds me of is someone dealing with a person who's disabled in some way, and pushing them to be able to be as capable as possible instead of settling on a smaller niche where they feel comfortable, if that makes sense.
Totally. And in a great sense it fits with Babs's MO when it comes to the Birds, a "rehab for broken heroes" as I think Huntress put it (though it wasn't a compliment at the time). She wants to help people, bottom line. Because of the Batgirl legacy, and most importantly because she took Cass in and genuinely cares about her, she's got a rather substantial emotional investment in her, and they are family.