Wow!

It sure sounds like you are confused and suffering.

Right now the most important thing is to aim for some measure of tranquility for both yourself and your children. I know you said that your wife is a good mother but the exposure to the arguments, bipolar mania, and drinking is NOT ok for the kids and it sure as hell isn't good for you or your relationship with the kids.

It sounds like you wife has a long way to go to achieve stability. In the mean time, limiting your contact with her and taking steps to make sure the kids aren't exposed to any further destructive behavior is your best move. That may mean divorce, it may mean having the kids with you more than they are with her.

If your wife is unwilling to pursue getting well, or at least stable, then it's time for some tough love. Acknowledge your mistakes (which you've done) and then distance yourself from her drama and protect the kids from any further damage to their mental health.
Don't mean to sound preachy but you did ask for opinions.