Its always hard if you have problems with someone at work. And it's really important to solve that afterall you might have to work with her for a long time.
The managment is a good idea, but you said that won't be possible at the moment.
So I know that might be a difficult thing to do, but maybe you could schedul an hour or two and talk with her. Somewhere where you won't be interrupted, but where you are still able to quickly get your manager, if it get's out of hand.
Tell her, what the problem is and make suggestions on how you can solve it together. Give her to room to explain herself and her reasons. Maybe she's struggeling with something and if you know about it, you could find a solution together.
The most important thing if you do that is to remain calm and respectful and give her enough chances to explain herself. Also don't just tell her what's not ok, but explain every single thing and how you feel about it and why and give her room to tell her opinion on the matter. Also maybe ask further, like why she thinks this or that.
Just be honest, understanding and don't critice her to directly and things should work out fine. It might even strengthen your team.
Though there is the chance, that it might go wrong, so best is to ask your manager first. The one who doesn't want conflicts. Tell him, that you want to have a talk with her to solve things. I don't see any reason why he would be against it and if you have his permission, nothing can happen to you if it goes wrong.
I hope this helps and that you can resolve this!
Sorry if I sound like a textbook, I wrote an exam in managment two weeks ago^^
If you have any questions about this you can always
pm me