Your ex is not a good dad. He'd rather leave his child in sole care of someone the day after a medical procedure where you might not be able to look after him properly? Honestly, he's a fucking dick. Absolute, fucking stupid dick.
Anyway, that said:
You're a great mum and you'll manage. Make sure you tell everyone about how ex hasn't stepped up after your op when you see them with DS in tow! And make sure you refuse to have him back if Ex ever needs it for whatever reason (though you'd take him if there was nobody else because you're not a dick like him, but I'd make him panic / suffer first!!)
I'd get a taxi to take him to nursery if there's nobody else, you could just ask the taxi driver to help if he needs getting onto the seat (any normal human being would, I'm sure). Then at least you can still rest!
Ask nursery to help get him back in the car at pick up time, whether it's you driving or a taxi. Our nursery will do this. Again, make it clear dad refused to help so unfortunately you have no choice.
Or, stay home and let him watch cocomelon all day, order takeaway and don't feel guilty about it!
As for the cot, you could always have him in your bed, or even just put the cot mattress on the floor for a bit while you recover if you absolutely can't lift. But I'm sure you'll be ok.
I was advised no lifting for 6 weeks after some abdo surgery a couple of years ago. I was alone with my 9 month old a few days after, it was fine.