I like the oath thing, and it's nice that Babs is taking this seriously and is going with this "well, if you're not going to quit I may as well help you" attitude.
The "I pledge to you my guidance and support, you won't be alone" business is lovely, but I feel like if you take out the Batgirl aspect of it, that's something she really should be saying to Charlie.
Steph still has a mom, whereas Charlie has no family and seems really imprinted on Babs, not to mention the Batgirl identity. (Not saying Charlie should be Batgirl, but she should at least get a chance to fangirl Steph and Cass.)
I also really need to see Barbara reaching out to Cass again. Because really, the last time Cass we saw Cass saying she wasn't going to be Batgirl anymore, Bad Things happened. Babs had better get going with some well-meaning bat-stalking.
I wish I could separate what is showing hints of becoming a great story for Steph and Babs from how Cass and Charlie have been left out and disrespected, but it's hard.
I have come to the conclusion that Babs ditching Charlie is the equivalent of one year into Dick being Robin, Bruce just says "you know what? I need to brood alone. Hey Dick? Go live with Clark." D: