I cried pretty much every AlAnon meeting for the first month. Yes, it's normal. That's the beauty of those meetings. It's a very safe place to let your emotions out. Most of can't give in and cry around work, kids, etc. But in AlAnon you can speak your truth, and cry if you need to. If you keep going, you'll find that eventually you don't cry all the time...you start to feel better. Even if the A is still drinking, you start to feel better. That's the truth.
I think finding work will be good for your children to see. They need a good role model. It's not unusual for Mom's to find work outside the home, whether it's for finances or because they just want to feel some independence. My friend went back to work at a particular store because she wanted the employee discounts! Reason doesn't matter, the kids will adjust fine.
Glad you're here...keep trying AlAnon.