Don't post often, but threads like these give me the rage!!
My MIL has dementia (not RTFT, but didn't pick up on your mum having that condition, from your OP at least), so cannot really be blamed for this kind of attitude. OH is an only child, so the duty of care here does fall very much to us, but dementia has the advantage that MIL will forget the carers ever having shown up by the time we get out of work each day and can visit for the "evening shift".
But if she is in sound mind, your mum is being a right selfish cow.
No compromises on this.
Tell her she has a choice for cover over the course of this holiday: either accept carers for the interim, or struggle on alone.
Either she will find "miraculous" reserves to survive independently (this is my suspicion, based on your original post - I reckon she's capable of far more than she's letting on), or she will acknowledge her dependency needs and accept support.
If she is compus mentis still, aside from the holiday, then shove her a load of ready meals, and if she can't be arsed to put them on on time, that's not your problem.
If she is showing signs of dementia, that's a different kettle of fish. As a first point of call, could you try ringing up every evening to remind her to put them on (rather than go around each and every day yourself), and start looking at support alternatives...? My position is rather softer there as, with the best will in the world, she could not then entirely support herself - which, btw, does not IN ANY WAY negate your need for a break.
If that doesn't work, it's SS territory (buy you'll have to lay it on thick to get any sort of blood from a stone there...).
It sounds from your post that mentally she's fine.
Show no mercy.
I only wish I could!