How to rank up as Omega

I only just really started playing Wolf, and I ended up being the omega in a pack of three other wolves.
The two alphas a beta and omega (me)
There is no way to rank up by defeating the beta. Should I find some way to make her "disappear"?
I noticed the beta has hunted more than I have, should I try to hunt more?
I can't play with anyone either, they are just to mean.

P.S
What interaction can you have with lone wolves? Any way to leave my pack and start a new one with a loner?

Thanks!!

1. Catch the Beta when their weaker than you (lower hunger/thirst, or both.) Challenge them to a fight and you should have good chances.

2. You can try hunting more THEN challenging the Beta; this might raise your chances as well.

3. There is no way to leave your pack.

Thanks you very much!
I actually defeated her once, I just have to keep trying.