I was in the same situation as you, a year ago... It is better to sell your car & buy another in Qatar rather than going through all hassles. You will not be able to transfer License... but have to take Direct Test process takes around 4 months.
With regards to your family, it is better you don't Cancel your UAE visa as it will give you & your family Visa on Arrival for a month & can be extended for another 3 months. otherwise you wont be able to get your family for atleast 8-9 months as you need 6 month bank statement to apply for Family visa & 3 month statement for family Visit visa apart from other documents.