That is a lot of time wasted on trying to make something out of nothing, now you have time to make it all up, to yourself and your kids. I am not a religious person, but I will tell you I have friends in the church, and they are a great place to go when in dire straights, you may even be able to get some support from them, to keep your home and get you and you kids fed. It can't hurt to try.
Also, if you are so lonely, invite the kids in to your room (if you are comfy with it), get them some sleeping bags and keep them as close to you as possible and remember, no one will ever take their place in your heart, and you will see it fill up in no time. Love yourself also, look yourself in the mirror and remind yourself who you are and why you did what you did. "I am a good person, I am done being walked all over, I am ready to care for me-not another person" and do those things, repeat them until you believe them, because they are true, they might sound stupid, but if you start living them out everyday, it will help.
Enroll your kids in a program they might enjoy, and try to make it around the same time, so you can take that time to enroll yourself into other things that will get you out and help you make friends, don't jump into a relationship, just make friends, someone you can call (if you don't already have this) to just talk when you are down...pm me if you think that might help
I am a 25 yr. old mother, who was in the situation your kids are in, not that long ago...mom and her boyfriend always fighting....believe me, your kids not matter how hard it seems, will be soo much happier that he's gone that they won't notice much else, just talk to them, they aren't as fragile as everyone thinks, if you just talk to them.
I don't have much more at the moment, but it will come to me and I will let ya know...and like I said, feel free to pm me.
Oh, motivation or not, you should go and get the P.P.O. now, for you-your kids- and even the dog. Also make sure you get the dog licenced and maybe tattoo'd (ear) or pictures so you can prove he's yours should you need to. But if the dog becomes a reason for him to keep showing up, seriously think about it....could it maybe be easier to just let him have it?? I know that might feel like giving in, but I'd see it as releasing yourself from all ties to him...and making you less of a target. But that's just me...