What should I consider when remodelling, with "Aging Care" in mind? For example, what's the best flooring for incontinence?

Personally, I don't care for tile of any kind: grouting always gets dirty (despite the seals) and falling on them is just one more major risk factor: aside from getting slippery, easily, it's a HARD impact surface. Ouch! So, sheet linoleum/vinyl is my first choice. Wall-to-wall carpeting, aside from keeping it clean is usually very hard to navigate over in a wheelchair, so maybe hardwood or bamboo floors. (I avoid throw rugs .. too easy to slip on.)

If I could make changes to the house, I'd put in pocket doors wherever I could so that you don't need to widen the frame, still have a real door, but one that's out of the way. Doors make me nuts, now!

This is completely aesthetic, but along the base of walls I found clear contact paper (or some matching the wall paint) and applied it just above the baseboards. Keeps all those wheelchair marks from marring the surface.

If it's within the budget, I'd get central air/heat. As we age, we're much more sensitive to the environment. And air filters. And water filtering at the tap.

I drool over a walk-in bathtub. A wheel-in shower would be great. (Neither will happen in this house .. no room in the bath .. it's TINY.)

Consider lowering all the reach ranges .. front-loading washer, side-by-side fridge. Waist-height access to microwave or other small appliances. Closet rods become harder to reach with arthritis or if limited to wheelchair or scooter.

My best advice: restrict yourself to a wheelchair (if you're not already), for a few days, and see what's inconvenient or downright dangerous. It's an eye-opener.

Just a comment on cork flooring. Much of it is layered over a base just as engineered wood flooring, so although water resistant on the surface, is susceptible to water damage when soaked. This type of flooring is not recommended for bathrooms. Larger porcelain tile with little grout would be good for easy maintenance, but sheet linoleum would be softer and warmer if floor is not heated. As far as universal design, it is a wise choice for any remodel, if not for our own use, then eventually adding value for resale.

The most important thing to start with is the bathroom, since it tends to be the room with the most risks for falls. Freedom Showers is a good brand of roll in showers, as they have sizes that replace a tub and they are easy to install right on the subfloor, without mudding or recessing, so installation isn't that difficult or expensive. There are also some great "Integrated grab bars" available now, that have a towel rack integrated onto the grab bar, so you get both. There is so much available now that looks really good.

Widen door frames if possible, to fit a wheelchair.

Ahhhh I forgot about the grab bars. We have the things everywhere! I mean literally, everywhere. Hallway, bathroom has about a dozen, one on each side of their bed, one on the kitchen doorway, one by the front door. Anywhere there is a possibility of anyone slipping or wobbling or just feeling like they might do either.
You can purchase GOOD quality ones on amazon and from places like home depot or lowes. We got our first 2 sets in a package, 8 bars for like 40$ from depot (this was 2 years ago tho). Had my brother install them, they're so secure you could hang an elephant off them and they wouldn't even wiggle, lol.

PS: I said 50 to 100k to allow room for a vacation or postponed dental work first!

Excellent suggestions! These questions are "pre-need."

When we redid the downstairs bathroom, we replaced the tub with a walk-in shower and a sturdy towel bar as a pseudo grab bar. That has failed, and we'll put in a real one next time. The family room on the first floor can become a bedroom when needed. We were already 50-ish when we remodeled, and did think about little things to make the house safer to age in.

Google Universal Design. It is a design concept that incorporates "handicap accessibility" into the home design that doesn't end up looking and feeling like a home for only the handicapped.

Ahhh, 100k in the lottery, first thing I'd do is go on holiday!

Seriously tho, for us the best choice was linoleum flooring. We actually JUST redid about half of the house we're in for my parents. The linoleum is padded so it's easier on their feet, it was "sheet style" so the floor in both bathrooms and kitchen is just one giant piece, no cracks or spaces between for anything to end up. Easy to clean, and hasn't stained from any um... accidents.
We added ramps to the front and back doors (dad's in a wheelchair, mom can't go outside without her scooter) as well as BRIGHT coloured "curbs" anywhere there is a step down or up. (She is also half blind, and just loves walking off uneven ground... or driving off it.) We also had a door moved to make it easier for them to get into the bathroom at night, and put brighter lighting in all the rooms they are frequently in (150w minimum, glad we could find those in LED lights!)

The only things left that I'd like to have done for them, I'd love to be able to put a cement path out to the "garden" so they could both go play with the plants. They are lifelong gardeners and the only things they can reach right now are the pots I've scattered on the end of the driveway. (8 tomatoes, 2 peppers, cucumbers, assorted dwarf fruit trees, wisteria and jasmine.) And I wish I could make the kitchen big enough for them to "help" me cook, but there's actually no way to do that, expanding it in any direction would cut into either bedrooms or hallways that lead to bedrooms.

The only thing I really regret is the colour choices of most of the rooms. My mom insists that "only" cream will work for any given room, where I wanted actual colours (not dark ones, but visible, lovely colours!) but since it was her doing the remodel, it was her choice. I won out on my bedroom only, mostly because she can't actually come see what colours I picked! lol

There are many options for renovations to make a home more elder-friendly but remember that whatever changes or adaptations you make you'll probably have to undo it if the house ever goes up for sale.

The best flooring is sealed cork. It is attractive, non skid, resilient and easy to clean. If you are looking for ideas on how to easily retrofit your home to make it barrier free and liveable, you can do it for much less than $50K. Start by taking stock of what your parents needs are. If someone is incontinent, you need to consider what they actually need. Are they completely incontinent, or incontinent because they are unable to get to the bathroom quickly enough? If they are unable to get to the bathroom quickly enough, they may be at risk for falls. Keeping the path to the bathroom barrier free; adding handrails; improving the lighting and even considering removing the bathroom door may help. If their bathroom is too far from their living space, evaluate whether or not a room change is in order.

If you give us specifics there are many experts on this site and many resources online about barrier free homes.