I actually feel sick OP, I actually can't watch this car crash unfold.
It can't be allowed to happen.
You need to sit MIL down and say the following:
We can only afford to pay $X for a property for perhaps the first 6m, maybe longer. It will mean that EVERYONE in our immediate family is already cramped. It IS unreasonable for ANYONE of any age to be sleeping on a blow up bed for anything longer than a night or 2.
We would NEVER expect you to sleep on a blow up bed, and we can't consider doing it to our DC either.
We DO NOT have the funds to finance ourselves AND you in a property big enough to have everyone in their own rooms which would be realistically required to make the situation even remotely bearable.
For this reason, for the sake of £75 it is better if your flight is delayed by a couple of months, so that we don't have you on a blow up bed, and can receive you properly.
We've looked at this every way we can think of, and it's just not reasonable for anyone, any way we try to work it currently. We've decided to delay your trip for your own comfort.
then all you have to do is to say, to every wriggle and excuse 'That doesn't work for us' and repeat.