Saying that to your DC is the opposite of helpful. Not only is he confusing them, he is clearly assuming that he will definitely be back. And, importantly abdicating responsibility . In spite of the fact that this entire situation is down to him.
Whatever you decide in the future it will be helpful to set some guidelines, especially for the DC.
Explaining that you are apart for the time being, saying you are not sure if you will all live in the same house again (not that you definitely wont), but that you both love them and will see lots of them.
He isn't doing weekends/bedtimes because ha has done fuck all about finding anywhere to have them. If he's such a great Dad it would be a priority. That's not giving up o the relationship. That's taking responsibility, giving you space and co parenting properly, albeit separately at the moment.
The DC will be far better with stability, and having time with you both. You'll cope, and there is nothing to stop him helping practically when appropriate, as long as it's not confusing the DC.
He is being selfish, and subtly pressuring you constantly. It is no wonder you can't process it . And I am not saying that this has to be the end necessarily.