When making your decision, there's only one question that you should ask yourself--what do YOU want to do? If you were on your own, without any kids to complicate the matter, then who would you choose? Who makes you happy? Who makes you feel treasured and treats you like the human being that you are?
You tried for fifteen years to make a relationship with your children's father work. You put up with verbal and physical abuse, and, I think, you did things that maybe you wish you hadn't done (By cheating to get back at their father, you lowered your standards of what was acceptable behavior, which, I'm sure, didn't make you feel good about yourself.)
You wanted to know "Why do I feel so guilty for not going back to my kids dad after he tells me he will change??" You feel guilty because there's a part of you that feels that you've failed at that relationship (even though there is only so much a person can put up with--or should have to put up with!). A large part of your problems is that you love your kids and, as a parent, you naturally want to give your children most everything. So, yes, of course, you want to give them their hearts desire (for you to get back with their father, even though, you dread the thought of doing it, let alone even thinking about it).
Don't let your children emotionally blackmail you. Of course, they want you to get back with their father. Most kids do--whether it's good for them or not. As kids, they don't know what is good for them yet, and frankly, seeing their mother being verbally and physically abused is NOT good for them! Your children begin to think that this is acceptable behavior and will one day either act out this behavior on their future mates or put up with it because they think that that's just what you do.
The beauty about kids is that they are more versatile than you might think that they are. Most kids like positive behaviors and words in adults, whether they'll admit it or not. Since they're wanting you to get back with their father, perhaps that is their way of telling you that they would like to see him more. That is something you can do for them without actually getting back with the man (providing that he hasn't abused them before in the past. Some word of advice--usually if a person abuses the mate, there is a strong possibility that they will try to abuse the kids. Not always, but it's something to be aware of.)
To help your kids accept your new guy, try spending a little more time with him doing fun activities with them (but only if you think this relationship might actually be going somewhere).
Considering that you have spent at least half of your life dealing with physical and verbal abuse, you should definitely try to see a counselor of some sort if you can afford it. He/she can help you deal with any residual issues that have resulting from your 15 year relationship (and also help you identify those qualities in yourself and the children's father that kept you in that relationship for so long--and that still draw you back towards it).
As long as you aren't jumping from one man to the next every few months or years, I'd say that you might not have to give up your new beau or take some time away from him, BUT I would suggest that you try to set up some ME time for yourself (if you can afford it or can find the time). ME time can be as simple as having a half an hour (at least) by yourself to read or take a bath or whatever makes you feel good about yourself OR it could mean going out with some gal pals once a week/two weeks/month or getting a massage or whatever.
I hope that these suggestions help.
The following are some helpful websites to help you deal with someone who is threatening suicide. Just remember--you don't have to do all of these suggestions. Do what is right for you: http://www.healthyplace.com/communities/depression/related/suicide.asp
One suggestion that I forgot to mention to you that you can do is immediately contact your ex's doctor and tell him about the suicidal threats of his (or you can go with him to the doctor for support AS A FRIEND, and stress that point). When talking to the doctor, see if he/she has any suggestions of agencies you can contact or people that he would recommend for a counselor.
Here is a link for mental health (also substance abuse) resources in Pensacola, Florida: http://findtreatment.samhsa.gov/ufds/detailedsearch_more?AD2=&ZIP=32501
Hope that helps!