DD was 2 and 10months when DS was born.
She was his first visitor. I had him at 12.30pm and she was there just after 5. She climbed right on up. I was just propped up but the epidural hadn't worn off quite by then so it didn't worry me. She was too busy with the baby to notice I was a/unable to get up and b/had a couple of extra tubes. By the time she came back next day after CC they were gone. It was exciting to have picnic dinners with mummy on the bed.
She had been at daycare that day so wasn't bundled off anywhere different. It was exciting getting to spend a few hours with people she adored in the few hours when they hospitalised me and DH was 6hours away at a funeral. She then got an impromptu holiday a few days later with Nan and Pop so that was even cooler. When she came home a week later there we were. She never once skipped a beat.
I had been on bed rest for many many weeks before that so she was used to having to climb up next to me and into my lap when i was sitting or otherwise just holding my hand. No way I could have lifted her when sitting. But I am starting with DS now. When he wants to be picked up I hold his hand until I can sit down and then get him to climb up. Same with his carseat/stroller etc.