I am gobsmacked BW.... really, sitting here with my mouth hanging open. I'm still with hitting him with a Solicitors letter that outlines all of his "offences"... leaving, OW, being unavailable, not being true to his word re: coming back when he said he did, shirking responsibilities, financial irresponsibility, etc, etc, etc. You don't have to have decided how you want to proceed with him, I just think he needs a giant stick of dynamite in the form of this letter placed firmly under his arse.
He is taking the piss. Massively. And you and the kids deserve NONE of it. You are not being selfish by thinking of yourself, at the moment, you are their only parent, their only carer, of course you have to look after yourself.
So he sent dd a birthday card. Big whoop. He does not deserve a prize. You all deserve better and he needs a giant kick up the whatsit.
(sorry for being a bit ranty)