i love my children with all my heart and they couldnt have a better mother. they were planned.
I'm going to go a little bit contrary to what many on here our saying (surprise!) And I don't "do" drama. I think relationships with a lot of drama are just asking for problems. For one raised in the 60's & 70's I'm actually an old fashioned kind of guy. I actually had to think about your post overnight before just blabbing off with an opinion (as I usually do
This (the above) is actually a very good reason to marry the woman.
"they couldn't have a better mother" If this is true then sounds to me like most of the problems at this point are yours - not hers. 8 years is a long time to have your lives intertwined & have children together.
As to weddings & not being religious - I'm a total atheist & I had a very small church wedding - mostly to please my mom. What's the big deal to you (a guy) whether it's a preacher, a JP, a Buddhist monk, a witch doctor, or a Wiccan Priestess. We're guys. Weddings are for the women - it's something you do for her - the guy's part is just to show up with a buttoneire and a smile; say "I do"; kiss the bride; and help make it a warm, romantic, & memorable event for her.
If she is being "sane" now & you are the one with the problems, you need to work out or just get-over your problems & carry on. Perhaps engage yourself in a little self-directed Rational Emotive Therapy. (a psycho-babble way of saying taking a good logical rational look at yourself, consciously making an effort to modify your behavior, and growing up! Sorry if that sounds a little harsh, but you asked.)
Mothers are looking for security, commitment, responsibility, maturity, and leadership in a man - the security/commitment thing could be a big part of what all her nudging you toward marriage is about with her (subconcious even). It's a natural thing on her part to want that (esp. after all this time) natural evolutionary instinct even - nothing wrong with it.
If you're gonna stick around, you need to provide her (& the kids) with that commitment - let her know that
you are gonna take care of her, the kids, & things through thick or thin - for better or worse.
Set a good example for your children of what a good, responsible, mature, emotionally healthy man should be. You should be steady as a rock for them. Be the leader in reducing all of this destructive drama in your relationship and your lives. I predict she'll love you for it. Consider it the best gift you can ever possibly give to her & your kids.
Another thought - If you split-up & she finds another guy, don't plan on seeing, being with, interacting, etc with your kids as much as you might think - despite what the court order may say. (Kids unconciously "know" this possibility too & it makes them insecure) From what I've seen the father/child relationship nearly always deteriorates/falls-away to some degree or another when the mom hooks up with a new guy - and you won't have very much control over this situation - you'll just have to take what you can get. The only thing you'll be guaranteed as far as your kids go will be writing a child-support check every month. Anything else you get re: your kids will just be gravy.
Like I said, I'm an old fashioned guy, but I believe it's a man's place in the relationship to take the lead (without trying to dominate her) in providing that security (financial & emotional) & letting her know you're gonna be there for her & the kids no matter what - even if you're unhappy with a few things once in a while or have a little "angst" here & there. That's the man's burden, women have their own burdens just as heavy.
If you're sure her "fooling around" thing is over with & was a one-time event, I say you should strongly consider going for it. She's not just your prospective "legal" wife - she's the mother of your kids & always will be.
Otherwise you need to just cut your losses (emotional & financial) walk-away, write your child support checks, give up half your stuff (if she asks for it or sues), admit your failure, live with it.