You're getting some great advice on here. Having a support network like this helps a lot- Miloismyboy's horse and mine seem to share a brain and though we live across the country from one another, sharing our struggles with our boys together has really helped me through some of the harder times. And yes, my boy has that one week out of the month issue too... so I have to disagree with Kevin as well. But still feel any woman can handle a horse as well as any man.
One other suggestion I have is for you to go and hang out a little at a local riding facility or with someone who has horses. Might be good for you to bring your girls too. It is good to see how different people react to horses and might give you a better idea of what is a big issue and what is just a horse being a horse. You'll also see some really ineffective ways to deal with horses so make note of what ISN'T working too. It is one thing to read a lot about handling horses, a completely different thing to see it in action. You need to know how big you need to get and what subtle things horses can do to prove they are the boss.
I think you're great for giving this mare a home and being really comitted to her. That's awesome. And don't beat yourself up, no matter how bombproof kid friendly and broke a horse is, if the owner doesn't know what they're doing, the horse will assume leadership. And we ALL started out knowing nothing so don't feel like you're the only novice in the world. Your open mind and willingness to learn are going to take you and Molly really far. Way to go!