It seem a lot of people get turned down the first time - it is always worth appealing - mobility allowance isn't only for people who can walk it is about people who need supervision when out and about. I would urge you to try again and appeal if you are told no.
I'm self employed but don't earn a lot at the moment so am claiming working tax credits. I applied last year but they turned him down, saying that he could walk. They didn't care that he can only walk for a few minutes before he needs to stop. The school isn't the nearest one, I looked for the one which was right for him. I went into depth telling them all of the things he needed help with, they didn't care. They didn't even speak to his physio whom he saw weekly but asked the GP who he'd not seen for years instead.
From yhour description it sounds worth applying for DLA - if he needs supervision when he is walking outside he may well get low rate mobility. If he falls into the road, which means he at risk he might also get middle rate care - which might mean you would also get more tax credits. I don't know if you work? If you are successful with DLA you might also get access to carers allowance. The DLA forms are not very nice and I would recommend getting advice on filling it in. However it sounds like it will make a huge difference for you.
I need to moan, sorry. I've sat and worked out that it's costing me £110 a week to get ds to school. He's 12, almost 13, so should be able to take himself by now but he falls over a lot so it's too unsafe. Most of the cost is because I have to go with him. I did apply for DLA a couple of years ago but they turned him down because he can walk. It was irrelevant that he is in pain after a couple of minutes or that he falls into the road, off the kirbs and down the stairs. ARGH!!!