first, you are most welcome in your 2nd home UAE
, it is better to hire car so you can go everywhere easly
in Abu Dhabi, you can try Al Rodhah Rotana apartment
Al Ain is calm city, there are limited choices of hotel in it, Hilton, Rotana, Intercont, AlMasah, and Mercure Jabal Hafit
it is better to stay in Abu Dhabi and Al Ain is only 150km from the capital
and Dubai is ofthe same distant
Abu Dhabi has two big shopping malls (others are small) Abu Dhabi mall and Marina Mall
resturant in Abu Dhabi for families (with private cabins): Pars palace iranian resturant, Indian Palace Resturant, maybe there are other resturants but these what I can remember now
But remember, once you are in the UAE for the first Time, YOU HAVE TO VISIT DUBAI, BECAUSE IT IS TOTALLY DEFFERENT FROM ANY CITY

لا تفكر تركب التاكسي الحكومي لانه كابوس .. عندك التاكسي الخاص افضل وبوصلكم للاماكن السياحه اسرع .. اما العين يكفيها يوم واحد عندك العين مول والجيمي مول وآخر شي روح المبزره