Hi Nether, I think there are two separate issues here. First: do you want to be apart from your H? If you do (and it sounds as if you do) then enough said. You are a grown up who can make her own decisions and if you want out then, given that most women hang on long after they should have left, I suspect your reasons are very good ones.
Second:can you cope? Yes of course you can. In the short term it will be stressful because change is always stressful, but in the medium and long term it will be fine. The more you can plan and put in place now, the easier the change will be i.e. plan where you are going to stay, sort out your benefits, plan childcare in the new location, brief your friends and ask for the support you need, all that sort of thing. Even if you can't do any of that (for example because he is violent and you have to get away now), fear of change is never a good reason to stay.
How old are you? Do you have previous experience of living alone pre-H to call on? If so, that will help, but if not, just work it out as you go along like the rest of us. If your priorities are your children and building a strong functioning family unit around you as a sole parent, you honestly won't go far wrong. Work out what you need to know in order to be independent and ask because knowledge is power and none of it is rocket science. If you can ask questions and understand the answers that is all you need to function independently.
Ask the CAB, your local council, friends and anyone else who might be useful. Take a notebook and write the advice down even if you feel silly doing it. No-one will care and when you are upset you often don't retain information well.
I taught a friend of mine who had never paid utility bills or had a bank account, how to deal with those after she split up from her husband. Easy for me and she felt so much more in control afterwards. If you don't ask, people will not know you need help and honestly, decent, normal people like to help others.
Just a tip. After talking to anyone official giving you advice always ask two questions: "are there any alternatives to this which I should be looking at?" and "what would you do if you were me?" These questions must come at the end, after they have said what they have to say. It is truly amazing what starts to appear when you ask those questions because you give them a chance to see you as a person, not a job. I use those questions all the time (including, garage, plumber, boiler repairman etc) and they usually give the best responses.
I suspect you may also feel guilty about breaking up the family. Don't. Your children will be fine with the change. Children are better at it than adults. I can honestly say that, although I can see some effects of my marriage breakdown on my children (they are very cynical about their father's motives for things for example), they are not traumatised and they are not deprived. They are certain they are loved and that we are a family even without their dad. Most importantly, as a family unit we are stable, calm and happy. That is what children need to flourish.
You'll be fine. I know from experience that making the decision is the hardest part. Everything else is just logistics.