The truth is even if you considered reversing the tubal ligation (depending on the method used) you still may not be successful in conceiving. I am not trying to be a downer, just realistic.
You mention that he is your boyfriend and that you are just separated from you husband of six years. It is awesome that you have reconnected with someone from your past however, you should really consider giving yourself time to mourn. Yup I said mourn because no matter what when wrong, whose fault it was, whether you left or he did, etc. you still need the time to mourn the lose of that person (husband) in your life. To get used to what it is like w/o him (specifically his quircks, his gestures, etc).
Wait until you are ready to make more of commitment and vice versa. Do not rush out and have a baby because you feel guilty. If it is meant to be it can wait.
I have been w/my current husband for 8 yrs. But we only got married last fall. I myself met him right after I split from my exhusband (father of my two boys), whom I had been on and off w/for 10 yrs.
I swore I'd never get married again (granted I was 26 when we split, rather young for that decision). I also was adament that I did not want any more children. As I said I had two beautiful, healthy great kids - whom (remember on again off again) I had up until that point raised by myself.
My current husband had hinted, eluded, and even asked me to marry him for several years, but I just wasn't ready. He also has no biological children of his own, but has been an awesome father figure to my boys who were 2 and 10 when we started dating. He has never shyed away from any aspect of their parenting. Diapers, being thrown up on in the middle of the night, discussing punishments, and all the good stuff, camping, fishing, etc. I couldn't ask for a better man for my children to idolize. So before we got married we had a long discussion about what our expectations would be. How we felt on all kinds of subjects. It was really nice, because I don't think we'd really done that before. I know I wanted to be with him for the rest of my life. I know he is an awesome dad and I also know he would like to experience having one more child. He never said a child of his own, cuz he calls them our boys. We agreed that we would have one more child. And we take what we get, boy or girl, god willing healthy, but regardless....so now after a 10 yr break we are expecting the last of the litter. Even when we were discussing w/the ob tying my tubes after my c-section, even then my husband said nope WE will have three children and three is enough. This was huge decision for me, especially because my ex and I started our family very, very young. I have been a mom since I was 17. Now my boys are 10 and 16. They are independent, we are pretty set in our family life - it was a huge decision to decide to start over again. One will be graduating highschool and the other on his way to junior high when this baby comes. Sometimes even now I am freaked out about it.
Please weigh all your options, I know just because it took me 8 yrs, doesn't mean that's what's right for you. Just be sure you've given yourself the time you need to heal and make the decision that's best for you, your boys and your boyfriend. Best of luck.