If your elderly mother is not in the house then she cannot go on the census form. I would imagine there are arrangements for people in hospital or other places. It is only those in the house on the 27th March. If she is not there you cannot include her.
Yes surely you need to include her - me and the kids will be on holiday on the 23rd, I can't just say no one lives at my house? Haven't seen the form yet but surely there will be loads of folk on holiday.
And the same if you're on holiday you fill it in for your house, the only excpetion I know of, is if you own a holiday home and that's where you are, you just fill it in for there . . .