Advice needed re:respite for Mum?

Respite-isn't that to benefit the caregiver? Who, who, oh who, pray tell is this "they"?, listening to her and not you?

I think that I might take on the role of expressing your justified anger for you!
grrrr.

Will think up a better solution for later, but for now, here is an idea.
Church functions do come in handy, and IF Mum's church had a 'function' during that time-a women's tea? Maybe you could drop her off. This plan would be good to do just before the move, getting her used to going out more, while at home you are MOVING, not shaking.
Then, go undergroud with the actual moving dates. Put on a calendar March 1st, when the actual moving date is a Sunday, somewhere in time. Just stop sharing everything with her to limit her stress, so she won't come back at you with more stress for you.
Plan a three day overlap for the last day to be in the old, and into the new. Moving expert here, sort of. There is just no way with Mum's needs, your age and stress level, and added stress of closing escrow, plus moving-physically demanding work- no way to do this in a day. Just think! You could be in the new apt. doing your thing for a few days before the actual big move, when Mum appears. Financially, it would be worth the decrease in stress to pay rent an extra few days. Don't tell anyone the move date so they won't spill it to grandma. Start sneaking out boxes-'Oh, these are going into storage til after we move', etc.
Congratulations! Good on ya, Jude. With your organizational skills, things will go better than you fear.