Thanks for all your replies.
I should point out that DP is not always like this, but it does happen occasionally.
In answer to your questions. No, all the housework doesn't fall to me - he'll do some at weekends, but until then he's the kind of person who picks up a tea towel from the hook and then puts it down on the counter the moment he's used it. He'll make supper (fantastic), but it won't occur to him to tidy/wipe as he goes, or that putting a wet pan lid on top of the mail is a bad idea. So he's a walking chaos-maker. He's also a lovely guy in many ways, and I'm not up for bitching about him, but he does seem to have a bit of a blind spot when it comes to my feelings.
He didn't seem as insensitive before we had kids but then we didn't live together, so we weren't in each other's pockets or under the same kind of pressure as we are now. And don't get me wrong, he's great with our son (I do pretty much everything for the baby), and doesn't mind cooking. He's really not an arse, but he can behave like one sometimes!
I love the sound of going swimming twice a week, Puntastic! I keep meaning to, but haven't yet as I haven't got my daughter sorted with a bedtime routine yet, so she falls asleep on me at around 8.30 most evenings.
My partner hasn't really had to look after them both yet. The baby is also exclusively bf and won't take a bottle, so she's pretty much strapped to me. I have a hair appointment tomorrow and will have to take her with me - with travelling times it'll be over 4 hours. God knows what I'll end up looking like! But I do fantasise about him having to look after them both for a week (no MIL allowed, which basically is an impossibility - she'd be here like a shot, taking over - but that's another story). Then he might have the vaguest inkling of what's involved.
I've recently also decided not to go back to work in September at the end of my maternity leave - it just doesn't make sense for us financially. But I really need to do something to turn things around for myself as I really do feel like a drudge, and wish my partner was a bit more empathetic.
I do think sitting down and having a calm conversation is a good idea. Trouble is, we've had them before and he seems to forget the content as soon as he stands up. And he wants them over as quickly as possible. I think he's uncomfortable talking about feelings. When I say 'I feel like X when you do Y', he often retorts in the form of an argument ('well you always do blah blah...') and things escalate/I don't feel heard/it all gets out of control. There can be a lot of eye rolling from him too, which tempts my red mist no end.
I'm not making him sound good am I? To balance things out I should say that I can be moody and have a sharp tongue sometimes. And I don't find living with a middle aged teenager engaging (and he knows it), so that can't be easy for him.
Anyway, thanks for your advice - I'm going round in circles. Definitely think a routine for the baby, the odd bottle of milk and some me-time will help me gain some perspective.