Poor mobility but not registered disabled

Your question was whether provision is poor for those with poor mobility

No you are not being unreasonable, provision is extremely poor for people who cant stand or walk that well

Bus stops dont have proper seating. Lack of benches all around. Shops are often exhausing to get around. Changing rooms often dont have seats in them so you cant sit down to get trousers on and off or shoes. Many other examples

Too old for PIP, but light weight wheelchairs are fairly cheap. Go with her to see her GP, he might write a statement to support a BB application. You don't know til you ask.

I get PIP due to my chronic issues, but she'll need attendance allowance. There are places like zoos etc. where you can hire wheelchairs and scooters. I hired one at the NEC in Birmingham as well.
If she can only walk slowly and in pain, then she cannot walk properly. I imagine she won't have a problem getting a blue badge.

if you take public transport then i assume its her that drives? if she has issues with her feet then is she safe to drive? i mean like can see feel them properly,move them fast enough to react/brake quickly

You/she can apply for a blue badge. She may also be eligible for attendance allowance if she needs care/assistance with other tasks.

Shop mobility schemes are generally helpful.

Cinema.

Theatre.

Open air cinema. Open air bus trips.

My DD has a similar level of mobility.

The answer is that you have to find places where you can drop her off near the entrance even if the parking is a little further away, specifically look for places where she can sit down frequently, and also consider places where you would be able to drive to pick her up if she has a bad day and can't walk back to the entrance. For your children, surely any play area that's not too far from somewhere you can park/drop her off with a bench she can sit on, is the answer? Take a picnic, sit and chat, watch the DC.

(And yes, provision of enough benches is woeful).

Does she have an access card? The criteria for getting one are less stringent than for a blue badge and it may open some more options.

She's 82 so won't get pip

But can she do it reliably and repeatedly? And how slow is she? If she can't do it in a 'reasonable time', which is considered to be twice as long as it would take a healthy person, then she is considered as unable to do it as far as PIP is concerned.

Most people take getting DLA/PIP as ‘proof’ that a person is disabled. But some councils also have a disabled persons card. My council has one, and this enables local areas such as zoos to get in as the disabled and carer tickets if you show this card.

I don’t understand. You meet half way between your houses, but you live 5 hours away and you go on public transport (although sometimes drive)? How does she travel the 5 hours to meet you?

Apply blue badge

https://www.gov.uk/apply-blue-badge

Your DM can claim this
Spend the money on anything to make her life easier
It is not means tested

https://www.gov.uk/attendance-allowance

I just had another thought: your DM could use Passenger Assistance on the trains if she doesn't already. You or she can ring up or use the app. Bigger stations will have station buggies (little milk float type vehicles) and smaller stations may have wheelchairs to transfer people between trains. Again, no need for proof of disability.

https://www.coam.org.uk/accessibility

https://support.legoland.co.uk/hc/en-us/articles/360024031592-Can-I-hire-a-mobility-scooter-at-the-resort

https://www.rct.uk/visit/windsor-castle/mobility-access-at-windsor-castle

https://www.windsor.gov.uk/visitor-information/travelling-with-a-disability

She sounds like she would qualify for blue badge.
Loads visitor places have mobility scooter to hire which my own parents were sceptical at first but then relaised they could keep up with grandkids on big country parks.

She's too old to get pip, but she should get a blue badge if her doctor can provide evidence that she can't really walk far. As far as "access to a wheelchair", neither PIP, nor Attendance Allowance (what those too old for pip can get) would give her that. To be provided with a wheelchair on the NHS she would need to go through her GP for assessment. I would be looking at possible wheelchairs to buy privately, or possibly a lightweight scooter? The other thing would be to look at somewhere she could hire one? There might be a local mobility shop which hires them out, or quite a lot of places like National Trust houses or council parks (big ones) etc have scooters for hire. Could this also work with her "not wanting" one, as in she could be encouraged to occasionally use one to keep up with the grandchildren, rather than told she's old and wobbly and needs to rely on a chair!

she won’t get pip at her age.

can you talk to the Red Cross about a wheelchair? They are usually pretty helpful. And Age U.K. will be able to help with benefits such as attendance allowance?

Little mobility scooter then. Probably give her a new lease of life.

You can apply to the council for a blue badge. There's nothing stopping you renting or buying a wheelchair though OP.

Have a look at attendance allowance.

Being able to stand and move alone isn’t a simple criteria. Especially if she’s in pain and slow and has to stop to rest.

Also a blue badge.

Walker with a seat attached may be a compromise if she doesn’t want to use a wheelchair but absolutely as mentioned above look at places where she can hire a mobility scooter.

But it also sounds like you need to be thinking much more about her future needs if you live so far away and cannot drive to her.

I can't disagree with anything anyone has said, but there's quite a lot of "stabbing in the dark" going on because I am not sure we have the information to give more informed answers. If she is meeting you somewhere, a wheelchair probably isn't the answer - who is pushing it because she won't be able to self-propel. Why can't your kids sit down for that long? How long? And where are these places you meet - how do you both get there? How does she manage at home - is that an issue? Maybe you could break down the questions into a bit more detail so we can give better guidance?

Call Age UK's helpline for advice on the Blue Badge form.

Or you can just work your way through the online application. The first page gives you the opportunity to apply for someone else

Apply for or renew a Blue Badge - GOV.UK https://share.google/oxfdLFrd2gzmEUboV

Just read your updates - I think it could be a good idea to find somewhere for a day out that offers wheelchairs or mobility scooters to borrow. That way she's not getting one of her own, which might feel like a leap for her mentally, but she still gets to go out and about. I don't know anything about the Windsor area but someone else might have ideas.
Tbh if she refuses to use a mobility aid to enable longer days out, I'd get a bit frustrated. I'm physically disabled myself and I have little patience with older people who insist on not using a wheelchair even for longer days out to the detriment of themselves and their families. People say "oh they're so proud" (not saying this applies to you/ your mum OP!) but that doesn't make sense - there's nothing shameful about using a wheelchair.