BRM05, hang on to your sanity! I know how hard it must be.
She just got this diagnosis and just got medicated. It's going to take many months before she is stable again, never mind the diagnosis - she's a newly sober alcoholic who has just blown up her whole life. Her meds are going to be a moving target. I'm in recovery myself (nearly five years sober) and the first year is a roller coaster even without new medication that may or may not be the right one(s). I'm glad I was single, I would have made a big mess of any relationship at the end of my drinking and in that first year of sobriety.
Focus on making the very best, full, fun, safe life you can for those kids. They deserve it and they will give you love and strength... between tantrums.
I do understand you wanting it to work. It's going to take time, you are also in shock and grief. Time will settle this out. You'll know when you've had enough and no one can help you get there - it's an inside thing, but it doesn't sound like there's a lot left to save at this point. You'll find all kinds of stories here, lots of wisdom if you read through the threads.
The wife...? Who knows. She may get better. May not. Statistics aren't really in her favor for long-term success. Addicts/alcoholics are nothing if not selfish. More will be revealed. I would definitely try to give her a very long leash right now, she has a lot to overcome and to prove before any trust is possible. The bipolar diagnosis may change over time, too.