I think it's wise to be proactive for yourself- in the event your concerns happen, but also- even if it's the relationship that motivated her- getting her own place and a job is a big step and that she pulled this off is something to consider.
While you anticipate the potential issues for your wife- and they are not unfounded, it's also possible she might pull it off. It's not unheard of that someone has felt expectations to be in a heterosexual marriage and later discovers same sex feelings. Anything could happen from now on- she may stay with the GF, or find a new one.
There was a chicken-egg effect with my BPD mother. She had low independent functioning and would escalate if she wanted something or wanted something done. So we'd step in an get it or do it for her, to defuse the situation. This reinforced her behavior and her helplessness, so each increased. It takes effort to do something on one's own, and so- BPD mother's default was to get aggitated, or threat, or yell, and so we'd do it. The other aspect of this was that BPD mother did not gain a sense of accomplishment.
Each of us were a part of this behavior. Us, overfunctioning for her/her underfunctioning. Now that your wife has taken this step- whatever happens is a large part up to her. You can only control your part- which is to stop overfunctioning for her- and in terms of what a counselor would say "get out of her way". Let her either succeed or fail, and learn from that.
Chances are- you have always been the sole parent in terms of a parenting role, with BPD mother taking more like the role of a teen babysitter if this involves watching TV with the kids. It will take some effort and additional cost to fill this role but that's the situation for single parents. For summer- older teens and college students are more available for babysitting jobs, there are day camps, after school summer programs. It will be good for the kids too- they get bored staying around the house all day in summer. During the school year, after school programs fill the gap between school and work hours. You may find your work production increases without the stresses at home.
If there is no returning back to the status quo- now is time to consult an attorney for information. This isn't filing for divorce- yet or ever- it's to know your options and what to do if you want to work in this direction, and how this situation may affect decisions like custody and alimony. Some states require a time period of separation. This situation may qualify as that. I am not a lawyer but I can imagine that being the main parent and your wife working, and also having another partner would work in your favor.
Note- I am not posting a run message. It's a "be informed of your options" message.


