Think about it - you want to pay 4.34% interest in order to make it easy for you to save properly - at deposit rates of 3.5% / 4%?
Your total debt = 209k = 60% of house worth 350k. You could be able to avail of low LTV discount rates (even 1yr discount tracker = 3.85%).
Your bank is not necessarily going to suggest the best option for you - you should get independent advice. Check out any Indept Mortgage Broker - they can tell you how much you can borrow.
The NB point is to repay the extra borrowings as quickly as possible - you don't want to be still paying for the car in 30yrs (and obviously take steps to avoid ending up in the same position again a year or two later!!)
Once you've your (new) mortgage back on track, then you can start thinking of saving/investing.