First of all, you need to realize that you can do this. it won't be easy, you will get lonely sometimes but you CAN do it.
You and the kids are your own family now. I realize it's not ideal for you and it's it's not what you wanted to have happen, but it did, so now you have to learn to look at it as a positive thing.
My kids were 2 1/2yrs and 13 months old when my ex left. I felt just like you, I was devastated and didn't know if I could get over it.
Trust me, you will.
Don't hide your pain from the kids, it's not fair to them or to you. You have to let them see you are hurt and that you deal with it. They need to learn how to do that themselves too, it's part of growing up. They already know you are upset, they can feel it, even if you try to hide it from them. And, if you try to hide it too much and not deal with it, you may end up yelling at them when you don't mean to. It happens, and you just have to learn to forgive yourself for these things.
As I said, you and the kids are a family now, just you 3. Don't worry at this point about when or if you'll have someone else in your life. The kids are the most important thing now. You can be both mom and dad to them, it's not easy but you can do it.
You have to deal with the grief, you can't make it all go away like it never happened. And you shouldn't feel shame. Did you do anything to make the relationship end? If so, forgive yourself, accept the responsibility of what you did and learn from your mistake. If not, then you have nothing to be ashamed of. These things happen and people deal with it daily. It just sucks when it happens to you.
You will learn to trust yourself again. You know deep down who should be in your life and who shouldn't. You'll recognize what is good for you and the kids and you'll know by instinct. Right now your hurt and pain is over riding your instincts and making you question yourself. But, have faith in yourself. Look at the good decisions you have made, focus on them. Know that you made good decisions before and you will again.
Just remember, your kids will grow up knowing you did all you could for them. My boys are now 16 & 17 yrs old. They remember what it was like growing up with me as a single mom and their bio-dad had nothing to do with them after the divorce. We are very close and they are very protective. We didn't have much when they were little, but they don't remember that. They just remember me taking care of them and loving them. They have grown up to be incredible boys, I'm really proud of both of them.
I met my current husband when the boys were around 5 & 6 yrs old, I had been a single mom for 4 years then. My husband and I got together, lived together for a couple of years, had a daughter and he later adopted my sons. They are now very close, they even call him their best friend. They hang out with him as much as they can.
Sorry this is so long, I just want you to know that it does work out. It just takes time. You have to allow yourself time to heal, time to grieve, time to adjust. You have to let your kids see you do all of these things. It helps them grow stronger and learn to deal with things too. They also have their own feelings about what is going on, even though they might express it by being cranky, irritable, crying, etc.
the best way to get through it is to deal with it with them. Love them as much as you can, cuddle with them, hold them and talk to them.
You will find yourself again. It might take some time, it might take a year or so. But that's ok. One of these days you'll look back and realize you did ok. you'll also realize you are a much better person and better off for it.
Good luck, I wish you and your kids well.