You can buy property in Dubai only in freehold area :
http://www.gulfnews.com/images/06/07/16 ... eehold.pdf
About mortgage you should have your own company in UAE or abroad minimum 3 years old , most important document required : 2 years Audit report for your company , 6 months bank statement .
If you dont have company don't loose your time because some ppl will tell you we can arrange it for you , just to take money , but when your case will rich the central bank it will come back : refused
New mortgage finder :

http://www.newmortgagefinder.co.uk/over ... dubai.html

You can stay you and your son in Dubai if you have employement visa only company in uae can provide you this , or your husband can be your sponcor if he have uae residence visa
you have answer to all your questions in this website :
http://www.uaeinteract.com/travel/visas.asp
Good luck
BEN