What a child wants in this moment, now, is not whats right for a child long term, and its your job as parent to make sure you do whats best for them long term, so you have actually put your child first.
It is not good long term for a child to have a dad who doesnt bother with them, a mum who is unhappy, or a mum forcing herself to be in an intimate relationship out of any reason other than she wholeheartedly consents and wants to be there. This way, dad has had a wakeup call and mum gets to be happy and that is better for their longterm happiness and wellbeing and what they learn about relationships.
When talking or thinking about seperation, people often confuse what a child wants to happen with what needs to happen. Its tough seeing your child upset, but a child growing up thinking an unhappy relationship is normal is much more damaging to them than being unsettled moving between houses. When people grow up as children of seperation, the consequences are things like them holding resentment towards their parents. When people grow up watching an unhappy marriage, they end up in unhappy relationships themselves, which can end up impacting them for life, abuse, poverty. They end up taken advantage of, they might even end up as awful partners themselves. Needs over wants. You are doing the right thing.
Also - if he's serious, then surely he wouldnt want you to rush into such an important decision and would want time for him to make it up to his kids and focus on them, making up for him being shit previously, working on earning your trust back, which takes months/years - not weeks. He's finding it hard and just wants it to be easy, he isnt interested in whats right for you or the kods long term or he wouldnt be trying to rush back in.