In my thesaurus loathe means the same as hate therefore I would think it is a pretty hard thing to come back from given that hate is a strong old emotion. I certainly wouldn't want to live with or stay together with someone I hated, kids or no kids.
I would certainly try some counselling though, however, and take steps to try to fix things and take separation as a last resort to know that I'd tried everything that I could to keep things together for my kids, but at the end of the day it is not healthy for children to grow up in a household where their parents hate each other and resent each others presence.
I speak as a child of divorced parents who went through a very acrimonous split (death threats, the works), it was not the 'easy option' but there is no 'easy option' unfortunately. Either way it will be hard. You both owe it to your marriage and your kids to try and save things but that does not mean you should spend the next 20 years of your life being miserable and resentful trapped in a marriage you hate. There is a limit to how far we should sacrifice ourselves, imo.