What are my rights? Used car dealer drama

[bluepony]

I bought a £20k used BMW X5 from a dealer (independent). The car has a knackered transfer box and they want to collect it and take it away to fix (which is good -ish)
This leaves me with no car (which is bad) and I am going to have to rent one (even worse).
I have two children in gigantic car seats and live on a farm so I can't rent a small cheap one as we won't fit in it.
The dealer say they have no idea the car will be gone for.
I am going to be several £hundred out of pocket renting a replacement.
Do I have any right to insist they pay for a hire car? They don't have a courtesy car, I asked.

[bluepony]

It got stuck in 4wd and won't come out and had buggered itself. Tyres are all wearing evenly (checked) and 4 runflats would be £1600!
I have just had to rent a car for at least a week. Not sure what lessons can be learnt here!

[bluepony]

lostkiwi said:

Ermmm.... aren't they permanent 4WD?

BMW said no - drive gets shifted front/rear or something as needed.

[bluepony]

bmw535i said:

How long have you owned it for?

Just over a month. But it had the problem when I bought it, only just got it confirmed at the main dealer last week though.

[bluepony]

It feels exactly like my old Mitsubishi did when the front diff was locked. Front tyres being dragged over the tarmac when turning.

[bluepony]

bmw535i said:

Why didn't you take it back immediately?

Because they assured me it was normal for those cars. And that they would put it right if it turned out they were wrong. I gave them the benefit of the doubt, not having driven that exact model before. It was quite subtle vibration at the time (now much worse).