If you have a downstairs bathtub without a shower, you can get
tub faucets that have hose shower attached that you could use.
places that sell medical equipment like wheelchairs sell shower
stools that are height adjustable, with plastic seats and
aluminum legs that won't rust.

if you don't have a downstairs bathroom, it may be time to
consider either remodeling the house to accomodate him or to sell
the house and move to one that is designed to accomodate a
handicapped person.  that may not be the solution your mother
wants to hear, but sometimes you have to do things that you don't
want to do in order to take care of your LO.

Johnny, I just can't see this being workable. It would be next to
impossible to get someone with mobility problems and dementia safely
into a kiddy pool in a kitchen. Its going to be incredibly messy,
really slippery, and water will end up everywhere. It will be very hard
to get and keep a pool full of enough appropriately temperatured water
to do wash someone - and then how do you get the water OUT of the kiddy
pool? Bailing with a bucket? And for your dad, most people in mid
dementia hate feeling exposed - the kitchen will not have associations
with bathing, and I'm thinking he will object to taking his clothing
off in the kitchen. Would you have him sit down in the kiddy pool?
Seems very dangerous in terms of the potential for falls (not just Dad,
but anyone trying to bathe him).

I'm afraid Denis is right - some kind of reno is needed. If you really
can't find a way to add something suitable to the main floor of the
house via either renovating an existing bathroom or even laundry area
where you could add a shower stall or walk in tub, or actually adding a
bathroom entirely - how about putting in a stair lift so you can take
him upstairs?
http://en.wikipedia.org/wiki/Stairlift

Mary G.