Please don't lie to your children.
Children learn how to have intimate and loving relationships from watching their parents - they are learning every minute of every day. If you live together but are not a couple, they will model their idea of what a happy / functional relationship is on you two - and that will be a fake/ non intimate/ distant relationship without real passion closeness or love. They will learn this in a million small ways.
One day they will find out and will know that the family they believed in was a lie - do you want them to spend most of their adult life in therapy?! Or worse, in dysfunctional unhappy relationships?
If they see you be a friendly, happy separated couple - they will learn that it is important to be happy and that even when things do not work out, it is possible to get on with life - that is a great thing to learn. You and your partner may meet new people and they will then learn about happy, real, true relationships.
I think you should have some counselling to talk all this through if you are seriously considering it.
Don't lie! It is really, really unfair and won't work. QUite apart from all this, you are closing the door on finding real love.
Enjoy the good friendship you have - and both of you need to have faith that you can find a better future as friends, with new partners if you want to.