Does your Mom have good credit and make enough to cover entirely the lease should you not be able to pay a cent?
Banks are willing to lend too much usually. I'd be cautious about trying to get a new M if you've already been turned down under those conditions. Even if you could come up with a substantial increase to the downpayment, I think you'd be living too close to the edge.
An Audi RS isn't much less, is it?
Present: 2013 M3 coupe (Azurite Black, Black, Piano Black)
Past: 2010 335i coupe (Monaco Blue, Cream Beige, Grey Poplar)
+ miata nut (2004 GT/LS and 2013 GS/Club Edition)