She's married I'd stay the hell away from any relationship with her aside from a professional one. Unless she has already filed for divorce there's no use continuing. The people saying you could be wrecking the family are right to a certain extent but none of us really know what this lady, her husband or her family are really like. For all we know her husband could be negligant, always away from home, abusive we can't just assume he's perfect for her and the kids the fact that therapy/counselling is mentioned and her seeking attention from other men means there's obviously problems within the household but we don't know of what nature. However I still think you should let them sort it out between themselves don't get involved, wait until she's made up her own mind whether it be divorce or not.
Secondly the whole superior thing is a problem, you really don't want to get into a relationship with a coworker especially one who works in the same department and is in the same chain of command (i.e. your boss). I'd assume you would have to inform her boss or someone higher up of your relationship, as well as other staff members judging you or thinking you're getting easier tasks. It may damage any chance of future promotions do you want to be known as the guy who got promoted because he worked hard or because him and the boss are butt buddies.
If you really want to continue with her than look into transerring into a different department/hospital so she's not directly working with you or around you. Keep your work and personal life seperate it's honestly the best way to go about it. Haven't you heard the saying "Don't dip your pen into company ink" or it's variations which all mean the same thing normally used for ladies "Don't get your meat where you get your bread". Pretty much don't look for any relationship in the place where you earn your money.
Lots of military's have fraternisation policy's for this exact reason because they know relationships between co-workers will almost always affect job performance.