She stated I wasn't eligible for the position.
What was her reason for saying that you were not eligible?
I've been losing her respect lately and she can't stand me anymore.
I hope she conveyed that information to you in a more sensitive way, but if you want to be eligible for the position, I'm sure you can work harder and achieve it. If you want the job, you should talk to her about what you can do to improve her respect for you.
She can always suck a dick and i think that's what she is doing with my manager.
It makes sense that you are upset about not being eligible for the position, however now you should turn that anger into motivation. If you work harder than maybe you can be eligible for it further down the line.