Hosting ILs (we do it a lot) is a source of great stress and consternation for me. So I feel your pain. With us, they come several times a year and can stay for up to a week. We aren't ever invited to visit them for a variety of reasons (from simply having no spare room - there's 4 of us plus a dog - to simply not being welcome to visit). But they have a tendency to treat us like we are running a 4 star hotel and gastro pub. 🙄
A few things, if you actually have a spare room and you will not need to give up a room and no one will have to sleep in the lounge, then I think it's reasonable enough to give them staying with you a try - this one time. If it goes wrong, then they are banished to a hotel in the future.
But this can happen only on the condition that: your dh does the hosting and organising. He does the tidying, washes and changes the bedding, does the food shopping (a great way to emphasise the enormous cost of hosting family for a week!), does the cooking (unless he takes baby and entertains them so you can do it in peace if you enjoy it), and he plans some activities out with them (possibly with baby) that you don't need to join him on.
One thing I've put my foot down with is that I no longer do a speck of cleaning for ILs visits. Dh is a people pleaser and will never say no, so he gets the joy of taking AL to scrape the kids yoghurt off the wall in the spare room, wash/change the bedding, clean the toilets. I also refuse to do everything constantly together all week. I truly cannot entertain people that long and ILs (all of them) are more the sort of pleasant small talk kind of people. They just want to chat about the weather. I can't chat about the bloody weather for a week. I make plans, hoist the children at dh and tell them to enjoy their day. I don't run around making their packed lunches and organising group visits to the garden centre.
Dh has quickly learned that having family visit isn't quite so enjoyable when he actually has to interact with them. When MIL last came to visit, he tried to escape to mow the lawn for 3 hours (it's a big lawn). I headed that off by saying I had something to do. I came back to him sitting in the kitchen watching a film on his phone with headphones in just to avoid having to interact with his own mother (which is awkward, but drove home to him that actually it's a lot of work to constantly entertain his family).
I would also say make your dh do the meal planning and shopping for their visit. Every time family come to stay, I get an exasperated sign and eye roll from dh because he cannot possibly understand why we have spent £200 on food shopping for the weekend. It's because they eat and drink us under the table. Once year I had MIL/her partner and BIL/SIL here for Christmas eve/day/Boxing day. For the 8 of us, for 3 meals a day, plus snacks, chocolates, biscuits, cheese boards, cases of beer, wine, port, whiskey, etc. for 3 days of constant eating and drinking, it cost us £800. Dh was absolutely flabbergasted. But that is how much they eat and drink and no one so much as contributed or brought a thing. It was like they were on an AI holiday. 😫If you need a reason to counter the whole FIL staying til the New Year, consider the cost, price out a budget, consider if you can actually afford that at Christmas time when you are on mat leave.