I think she committed to, uh, committing, when Dawn asked for the guy back... At that point I think she was only contemplating it, and maybe grabbed the forceps for simply a weapon, in case... Once Dawn changed things and demanded that guy back, Beth said F it because things weren't going to be good.
I don't think the goal of the forceps was initially to stab Dawn though... Just so she had something because she was going into it unarmed. If anything I think she felt bad for Dawn, to a degree, and was trying to reason with her that this is life and it's depressing, and you have to deal with it.
Dawn kind of betrays Beth in a way. Takes a liberty and a last parting shot, by asking for Beth's friend back as compensation for losing her "ward". She'd professed all along that the wards were simply a means to an end for her to keep control, while keeping people safer than being out on the street... Beth maybe bought into that to some degree, but obviously still felt it was wrong and that Dawn was just doing it to keep the peace... Obviously Dawn wasn't. She was just another POS like the Governor, or the Termites, or whatever. Just another person taking advantage of the world as it is rather than facing it for what it is.
Beth's last straw mentally was knowing her friend was going to probably not make it out of there alive. She snaps, she stabs Dawn and gets shot in the process, etc., etc. It was her, "**** it" moment.
That's just how I see it though... no clue if that's how it's intended because I agree it's not explained terribly well. I think it's subtle, at best.