I'm in a similar position in that I have two lovely boys (3.6yrs and 22mos), and I would love to try for another baby in a year or so when DS1 has started school.
DH won't hear of it, though, unless I can guarantee him a girl who'll sleep through the night from birth .
I'll be 40 next year and I've had two MCs and difficulty conceiving in the past, so even if we do give it another go, it might not necessarily happen. I'm therefore trying to remain philosophical about this - if it happens by accident (not accidentally on purpose, I hasten to add) then that's great, if not, then at least I have my two extremely precious boys. But of course I don't know how I'll feel in a year's time when DS1 is at school and I'm a bit closer to the menopause.
How old are you by the way?
On a practical level, can you hire a cleaner to make the house tidier? Perhaps your DH thinks that if the house is so messy with only two children, a third will tip it and him over the edge.
In the meantime, your youngest is still very little and your hormones might still not be completely settled post-birth. Can you not give yourself another six months in which to talk this through with your DH and work out exactly why it means so much to you have this third child?