This is probably not very practical financially but the only thing I can come up with that won't offend is to say you'd like all four of you to have a weekend/week away somewhere and stay in a (clean) apartment/cottage/hotel whatever. But probably not do-able if FIL is sick too.

I think the mess is a more difficult issue than the diet. If they're nice people they're not going to take offence about you wanting to feed your baby what you want plus you can say how everyone's just very cautious these days about food/allergies etc. etc. and your MCHN has said he can only have this, this and this and yes, you know it's a bit over-the-top but you'll feel really guilty if he gets sick etc. etc. etc.