Sirius grinned widely, then changed form, becoming the dog being referenced here. He put his front paws up against Remus' chest and seemed to be wanting to lick his face, tail wagging, but then he moved away again, jumping right up on the bed and curling up around Harry, nuzzling him. So, yes, that was essentially the life they had been leading as of late.

His tail wagged and then he changed again, his arms around Harry instead. "What kinda story are you feeling, golden boy?"