Mahhty - so glad you've met someone who excites you. She sounds awesome.
In regards to the kids.....don't introduce her. Not for at least six months.
I know that sounds like a ridiculously long time, and I know it's important to get a sense of how she is with kids. But let's face it: statistically, the odds of any new relationship fizzling out in the first six months is rather high. And your kids DONT need to grow attached to, and then lose, a succession of girlfriends. Breakups hurt kids. So take it slow and don't introduce the kids until you are pretty sure she's a keeper.