Man that is a helluva thing... you're a bigger man than me in allowing your ex partner to have their new partner around.
I'm sorry things did not work out in the best way for you, don't crucify yourself too hard for not " getting it right" the first time in the soulmate search.
I would for sure say at least your relationship granted you a wonderful opportunity: to make sure you raise those kids right . That kind of love is special and will last the rest of your life. Don't let your disappointment (is that the right word to use here?) with your love life keep you from showing them how much beauty comes from loving someone else. You get ONE chance to be a good parent , you don't want a fractured relationship with your children when you're older nor do you want to be full of regret that you should've done things " better" ( hi mom and dad"). There are many different types of love, if romantic love is absent in your present, fill your life with as many other kinds as you can. Good luck.
* Edit* read the follow up posts, you MUST take steps to ensure you won't just be forced out on a whim/ through your life being made very difficult. Your children need you , you need to make 100 certain there will be no issue in your having a positive impact in and on their lives