It does get easier, so don't beat yourself up as it is tough on everyone adjusting to a new arrival.

Like Tilda mentioned, my DH used to take both of them out on a sunday arvo so I could just go and sleep for a few hours.
In terms of your older child not having a nap, maybe all 3 of you could go lie down in your bed. I sometimes would feed DS lying down, and because DD was with us, we'd all snooze. Othertimes, I would just put a DVD on, and lie down on the couch. Occasionally she would still fall asleep.
TV got a major work out in our house in the first year (it still does occasionally).
I also got a good carrier that I could wear DS in for a couple of hours, as at that age, he wouldn't sleep in the cot, but would have a good sleep in the carrier, and it meant I had hands free to play with DD.
Also, we had a good double pram, so we went walking alot too.

be easy on yourself