I slept on the sofa for first two nights after giving birth. And lay on it for the first two or three days. It was only because I wasn't able to get upstairs or go anywhere and the bathroom is downstairs but honestly it wasn't that bad. Depends what sort of sofa or sofabed you have.
When I had family over from NZ to stay recently, I offered my room (I was going to share with DS) but they declined and said they didn't want to invade my space and stayed on the sofabed in the living room. TBH I found this more of an invasion, they were just there the whole time. I hated trying to keep DS out of the living room in the mornings when they were still asleep or feeling I was disturbing them if they wanted to go to bed sooner. I also had their clothes and things in my living room so it didn't really feel like my space.
I'm sure if your PIL are staying in your room (if that is what you would feel best with) then they would no doubt retreat to your room if you need privacy as they would feel a bit awkward hanging round during MW visits and awkward feeding, they could take your older child off to the park or out for a walk during these times. Most PILs will make themselves useful during this time and respect that it is difficult.
Work out what is best for you, especially sleeping arrangements, discuss all the permutations with your DH and ask him to support you and accept that it may be very awkward. Ask your DH to discuss things with them like privacy for feeds and how you feel about this. Your PILs will probably want to help out, so if they ask if there is anything they can do, tell them and let them help. Get them doing the laundry and washing up if they ask and don't be afraid. Whatever you do, don't try to be the perfect hostess and entertain them. Prepare some tourist information for them and ideas of local places to go, especially places they can take your DS. Make them useful.
Plenty of people have their PILs to stay during this time and get on just great.