Still “seeing him” and living in the same household is not the same thing. When kids prefer their parents are not together anymore, they don’t stop wanting to actually see the parent. They just prefer to not live in the household where dysfunction is rampant and parent is intoxicated the whole time and/or parents don’t get along. When your daughter tells you “I don’t want to live like this”, she’s not telling you “I hate my father and never want to see him”. She’s telling you that living this way is unhealthy and she recognizes it.
If you are to separate, I am not sure what you mean by you getting together with your husband. It wouldn’t be a separation then.
Do you worry how he’ll be lonely without you more than worrying how it effects your children to live with an addict who won’t seek help? It effects them for life.
Also leaving someone doesn’t mean you have no empathy and compassion for them or become callous. You can have compassion for him yet not live in the same household.
Of course you could stay but I hope you at least continuously seek help for yourself and your kids