Wow Chris...You opened up a whole bunch of cans of worms all at one time. The answers to your questions could probably fill an entire book. So...where do you start out?
First, welcome to the board and please know that you are among friends. Regardless of your individual situation, I can guarantee someone here can identify with all your issues. Finding a professional to talk with is probably the best thing you can do for yourself and your children. If your wife has already made up her mind to dissolve your marriage, and it sounds like she has, the best thing you can do is formulate a plan to get on with your life without her.
It does sound like you are having a problem with anxiety, and the medications you mentioned being prescribed are appropriate for helping to keep your moods stable over the short-term. The "side effects" you mentioned are probably more from the anxiety than the medication itself. Try taking them as prescribed and give the drugs an opportunity to work as they are intended. I'm a firm believer in helping out the chemical imbalances that our emotions can create when we are confronted with extreme stress, grief, feelings of failure, etc... that come with the dissolution of a long-term relationship. Stability is not just important for your own sanity, but it is also important for you to be able to help your children understand and cope during this period of transition. One thing you want to avoid though is taking any OTC(over-the-counter) or homeopathic remedies if you are taking prescribed medication, as you want to avoid any problems with drug interactions that might come from mixing the two.
I might also suggest checking to see if there are any local support groups in your area for single parents, like "Parents Without Partners," where you might find like-minded people in situations similar to yours, that offer resources and activities that can help you thru this period of transition.
Believe it or not, this really isn't the end of the world, only the way you knew it for a relatively short period of time. Ten years out of an entire lifetime really is just a minor splash in the bucket, so you've got to get on with a whole lot more living to do ahead of you. Try to keep your focus and mind on all the milestones your children still have ahead of them in their lifetimes. I've been in your shoes myself, and I've had to start all over more than once, so I am well acquainted with the concept that the end of our books are open to rewrites up until the very last minute. My life today is completely different than I would have predicted it would be only a year ago. Take things slowly and the details will work themselves out eventually.
Most of all, remember that you always have someone here that's willing to listen or offer a shoulder to cry on if that's what you need. Good luck to you and keep us updated.