Legally, until there is a custody agreement or order by the courts, parents have equal custody of their children and are supposed to have equal access, though I know that doesn’t always happen.
I am not positive, but I believe that since you adopted the oldest child she is considered legally yours. I am not sure how that would work.
As far as her leaving you and moving that far away, you have the right to tell her that she can not take the children with her. My advice to you would be to start documenting everything now. You stated that you are very active in their lives, caring for their daily needs emotionally as well as physically and financially, so you have a good chance at getting custody. Just my opinion, but you sound as though you are more worried about losing the children than your wife leaving you. That’s not a bad thing, just an observation.
If you are ready to separate from your wife, fight for custody and keep the home, I would suggest talking with an attorney about “Divorce from Bed & Board”, since she is making your life finacially unbearable. This way she would have to leave the marital residence. Also have a separation agreement drawn up giving you primary physical custody and joint legal custody of the children,(if you can with the adopted child), child support and go ahead and put equitable distribution in the agreement. If she is moving and currently holds no employment, it may be to your advantage. Talk with her about signing this and I would make it sounds as though you are doing her a favor, since she can not provide or care for the children while trying to get herself settled in a new place. Kind of sneaky, but hey, if it works, you will have custody and the home. You will still have to split everything with her but the big issues are taken care of.
Good Luck and keep us posted!