How do I get sole custody of a child in the state of WA!?

My GF and I have a daugther (10months) and things really get worse by the day and I just stay there because of the child and what may happen to our child if I would leave!
I have to add that I am a german citizen and want to move back to Europe, at best with my child!
To the mom is to say, that she is a sex offender on probabtion, an alcoholic (which already is in conflict with that probabtion) and very much bipolar as well. But I guess that is in this state not enough to gain sole custody of the baby, so I could provide her overseas a way way better chance of a decent life??? OR?

(JA the plain logic says, "hey you have to get this child away from her", I heard that often enough, but when is justice ever logic? So I ask just for further, maybe more specific, opinions)