At a guess I would think that it may have something to do with being under her mother's eye and (possibly sub-consciously) feeling she has something to prove to her mother about her home making capabilities and skills. And there may be a slight feeling that if she isn't super-wife she's letting you down (I'm sure you
don't think this).
When all is said and done three people make 50% more dusting, vacuuming, laundry, tidying up, cooking, dish washing, etc.etc., than two people.
What about co-operating with her to draw up a time table for household tasks with "me time" built in eg sitting down with a book, or going for a walk, for a couple of hours one or two afternoons a week.
You could also discuss priorities - some items of clothing such as socks, underwear, etc., have to be changed daily but if an outer garment isn't dirty does it have to be washed after a single wearing especially if the wearer showers every day? Ironing can be kept to the minimum - underwear, night gowns and pyjamas, bedding, jeans or sweaters doesn't really need ironing, Shirts hung on coat hangers after washing need less ironing and instead of Mrs RB having to iron a load at a time, one could be ironed as required and, as I suspect you're old enough to have been in the military, you should be expert at doing that
Bathroom towels don't really need to be changed everyday. Bathrooms and kitchens need to be cleaned daily both for hygiene reasons and because it's easier than it would be if they were left for days but unless you are a really messy family the other rooms should only need a bit of daily tidying with a turn out once a week - perhaps one room a day. Would MiL be able to do a bit of light dusting, veg prep for dinner, setting the table for meals, etc?
If MiL needs a lot of assistance with showering, , etc., is there any help you could get for that? Say through a referral from her doctor or an organisation or older people.
Just a few ideas if they help. It's important that you take care not to come over all judgmental when you raise this. You don't want your wife to misconstrue and think you are criticising her rather than trying to help. The really difficult thing for your wife will be learning to say "No" to her mother. If MiL wants to go out you wife should be saying "Well, if you help me do ..... in the mornibg we can go out in the afternoon"