Please don't stay 'just for the children'. Its a massive burden to put onto them that you 'put up' with each other just for them. Your children will not thank you for it.
My parents lived in the same house together but clearly hated the sight of each other.
Nasty comments between each other they thought the children wouldn't understand (we absolutely did understand, if not the words definitely the meaning) were really cutting. They rarely stayed in the same room as each other but both were as happy as anything explaining 'oh your Mums just popping round her friends' or 'dads got to go back to work...at 10pm at night' when in reality the situation was so bad between them they couldn't stay in the same room as each other.
It was hell living like that for years.
Eventually it drove my Mum mad and she used to shout that 'we should be grateful for what she has sacrificed for us to live together as a family' 
Don't think for a second your children don't know that something isn't right. They know far more than you realise.
Children seeing their parents living separately but being happy human beings is far better than watching the parents they love being nasty, unhappy, spiteful and selfish trying to grind each other down to get the other one to give in and be the bad person and leave the family devastated.
What lesson do you think you are teaching your children? My mother believes she was teaching us never to give up easily and always work through everything. I saw it as she was teaching us it is ok to be nasty, vile, spiteful about someone who is loved dearly by their child and then put the blame onto the children for the situation because it was all done 'just for them'.
I still struggle with my childhood and how miserable it was, its made worse by most people I know (including DH) recalling lovely summers with their families, everyone happy together on holidays at Christmas etc. I have none of those types of memories because my parents hated each other for so long they just couldn't act like a normal couple. Everything ended up a competition on who could outdo the other one.
Its a better lesson to teach them that sometimes people need to follow their own path in life and that's ok because staying means someone is unhappy and we don't want anyone to be unhappy just for us.
Explaining a separation to children can be easier than you think. Explain that Granny and Grandad (or favourite cousins/aunts/uncles etc) don't live here with us and we still love them lots and they're very much an important part of the family. Mum/Dad are getting their own house/flat and we still love them exactly the same as we do and like Granny/Grandad they're still a very important part of our family.