You're not being at all unreasonable. I have never understood the need to visit someone as soon as a baby is born, most especially if there are unmitigating circumstances. Agree with TinyTear - 48hrs is still too soon, and personally, I'd ask them to hold off for a least a week.
My MIL was a bit like this - she lives really close and constantly popped in - I'd had a difficult birth, was really struggling to B/F, my own Mum lived miles away. If MIL had popped around with, say a casserole, or offered to cook a dinner, or do a bit of shopping or pop the hoover round, maybe, that would have been so lovely (I've done all those things for her when she and FIL have been in poor health). But no, she just popped in to cuddle new baby, I was still in my dressing-gown, very painful stitches which made it difficult to walk, but I'd end up making lunch and cups of tea for her whilst she just sat on the sofa, cuddling my new baby who was screaming for a feed (which I was finding difficult to provide). Very, very, very stressful.
So OP - stick to your guns. If you don't want visitors in the early days, then say so. Tell them when you are ready for them, and not before. Unless, of course, they are going to offer some practical help . . .
