@phenom13,
I'm not a doctor but I've had experience with depression. What you've described doesn't sound like what I know to be depression.
In any case, my experience tells me she isn't going to get better with out meds. It's caused by an imbalance of brain chemistry and she needs some additional chemicals.
If the side-effects of one drug are too much for her, she needs to switch meds. There are lots of drugs for depression and it may take a while for her to find the right one, but if she's trying, you need to be patient.
If on the other hand, she won't make the effort to treat the condition she knows she has, you've got a tough decision to make.
From what you described, you've been a solid partner so far (maybe even too easy on her - again, depression doesn't make you cheat), but if there's no end in sight because she doesn't want to work towards one then you can either resign yourself to being miserable for years to come, or move on. The latter isn't as easy as all that, but it is a viable option.
You fell in love with someone years ago. That person is now considerably different from the one you fell in love with. If the change is something she cannot control, then I can see you coming to the decision that you can't abandon her. You need to convince yourself, before you make that decision though, that she cannot control or mitigate the change.
I don't think that's the case.
Taking up with some other guy is something she could have controlled, irrespective of her depression or thyroid.
Finding and sticking with meds that can control her depression is something she can control
(Not to beat a dead horse, but mood swings are not classic symptoms of clinical depression)
Bottom line is that when you marry someone you're not making a pledge to give up any personal happiness if necessary.
You say you love her, but do you love her as she is or as she was?
You have kids and that creates an entirely different dynamic. You need to sacrifice far more for them than for your wife, but there is a point where it is better for the kids that their parents are apart than if they are together. You just need to make sure that you don't use them as an excuse for your own desires.
You say you're going to seek professional help. Good idea, and if so, you don't need me to tell you what to do.
Just remember, your wife is not a mindless slave to the condition of depression. It's a tough condition with which to deal, but it can be dealt with, and if she is one of the rare few that no meds can help, you need to confirm that before you resign yourself to a life of woe bought by a sense of duty and honor.