Practicalities for E-Bike puncture repair

I appreciate your mum might not be very srong but why would she not be able to turn the bike over by laying it down and titling it back upsidedown onto the seat/handle bars by lifting the wheels. If she can't right it from a horizontal position at all then she will have bigger problems than a puncture.

I have used the injected puncture repair stuff on a commuter bike and it was very effective, left it in for over a year with no problems. It was very noticable at the start of a ride though (especially if left for a few days) as the liquid goo had all run to the bottom and left the wheel out of balance, took about 1/2 mile at reasonable speed to feel right again

Better to minimise the chance of having to fix it, rather than work out how. I'd recommend using Slime sealant, either the pretreated tubes or just buy the can and treat the existing tubes with it (I get it at my auto parts store here in Aus).

The suggestions to use Schwalbe Marathons is good, but they're tough to put on or off and as good as they are they won't stop a 3 inch nail, which happened to me last week. Slime will make the tubes self healing and is guaranteed to work for two years. I put the Marathon Plus and Slime tubes on a Gazelle e-bike, because having a Nexus hub and roller brake plus a front hub motor made removing either wheel complicated, plus all the guards and rack made patching a tube in situ more trouble than it's worth, so it was good insurance.

I fitted Schwalbe Marathons to my cargo bike, not because I wouldn't able to replace a tube if necessary but because I'd rather not have the hassle or the need to carry a spare tube and a spanner. I do however carry an aerosol puncture repair with me just in case. I've never used one on a bike but I have used them both on motorbikes and cars as a get you home repair, always with success. 

An alternative would be a bicycle recovery service (like the AA / RAC but for bikes). E.g. https://www.eta.co.uk/breakdown/bicycle/

(no idea if they're any good, was just the first result on Google)

This is a dilemma indeed. As mentioned by others - upgrade the tyres to Marathon Plus or Big Ben Plus or similar. Check the pressure reguarly. 

What type of gears does the bike have? A hub gear, especially a CVT like NuVinci is a sod to remove (and re install) the wheel in the rain on the side of the road. If it's a quality eBike it will have hydraulic disc brakes so that adds another 'challenge' when putting the wheel back on. 

You can buy double ended inner tubes (Rubena manufacture them) These can be inserted without taking the wheel off and are therefore recommended for cargo bikes especially. 

Or you could use that inner tube sealant stuff - but I have never used it so can't say if it works. 

The final piece of advice; if you are an urban cyclists know where your bike shops are - so you can push the bike to the nearest shop if you get a flat on the way to work etc if you get stuck. 

I've customers with e-bikes.... those with cheaper models I've retro fitted marathon plus as most quality ones already spec those out of the box. I did the same recently to a Gazelle Cabby which only had Land Cruisers on the rear. I also have a few who have asked for slime tubes and Marathon plus tyres

sounds like you need a good quality double kick stand

https://ursus.it/shop/urban-city/big-foot-87/

Get puncture resistant tyres or even tubeless.
Get a lift or taxi if you get a puncture.

Although if the bike is laid down on its side, it should be easy to remove the wheel.

Only my anecdotal evidence, but I've ridden both normal e-bikes and e-cargobikes for years and never had a single puncture even though I've covered far more miles on them than I do on my road bike, roughly 10-15k a year

Why?

The tyres fitted are of much higher quality, usually with puncture protection built in, Schwalbe Marathon seem to be favoured by many e-bike manufacturers. 

Instead of worrying about carrying an item unlikely to be used bar the very odd occurence I'd ensure the tyres fitted are of a similar quality as mentioned above.