The vast majority of women are not disabled four weeks after giving birth. The main problem is tiredness, especially as any support you get tapers off after the first few weeks.
In these early weeks, if there was anything I really wanted to do, I would drop everything else and focus on that one thing. Preparing one meal for guests does not mean preparing three meals for days on end. To say that it is out of reach for a fit and well 4w pp is not really true.
Even with the idea that they invited themselves over, the OP posted at 7am. This is plenty of time to get sorted. Unless you live in a seriously rural area, it's not that hard to run to the shops, especially when there are two adults involved. One can shop and the other clean. I never really got the notion of the weekly shop as I like to shop everyday for just what I need.
The other thing is to be in control of the invitations. If you don't invite family, then they will invite themselves! Be proactive! When I was a child back in the 70s, extended families would just turn up - no phone calls, no social media. That's why my mum always had a tin of salmon in the cupboard and the ingredients to make scones (12 minutes in a hot oven).
I think it is quite nice to have relatives to sit around for a whole day. It means they are enjoying your company! They are your family, not just your DH's. Tell them when they are out of line. Ask them to put their cups in the dishwasher ("would you mind..."). Tell them you need to have a nap, because the biggest problem you have is tiredness and you need to make up for broken sleep ("stay as long as you like, but I just need to have a couple of hours of shut-eye").
I read these inlaw bashing threads and always wish I had these problems. Mine live thousands of miles away, and my own family 400 miles away. I would love to complain about their visits, but they are several years apart.