Honestly... yes people probably didn't realise it was a wheelchair rather than a pushchair.
But switching to a wheelchair you're unlikely to get much more joy, other people on the whole couldn't give a fuck as they were there first, and your presence is going to inconvenience them.
That is even if they look up from their 'traveller trance' and notice you exist.
It's also not really appropriate to fill the whole accessible space with non-disabled family so if you go for a chair that can't be folded, rather than fold chair, sit in normal seating, you are going to have to split the family up to travel on trains. There really isn't a way around that as the accessible spaces do not take into account the concept of disabled people having friends (particularly, disabled friends!) or family!
I've had people rest their bike against my wheelchair (so it constantly bumped and joggled me), occupy the flap down seat so I had to sit in the aisle (they were shifted by the ticket collector)...
And then there was the day that, as I got on the train, someone dumped a couple of large bags in the wheelchair area. I said 'Excuse me, I need to get into that spot' and got a very unpleasant sneery response:
'Well I was here first... what are YOU going to do about it'.. as he strode off down the train.
I shouted that I'd move them, and he just muttered 'yeah right' as he vanished.
So I did. Was quite a simple matter of hauling them from in front of me, and then out the door back onto the platform.
Long story short, he wasn't very amused at finding his stuff still in X when he reached Y. Fortunately for me, the other people in the carriage were on my side and a member of staff had turned up just at the right moment, or I think I was going to get thumped.