Is it worth visiting with family, considering most of the stuff, transport and tickets to any parks, museum, burj khalifa,etc are very expensive?
To be honest, "worth" is very subjective. Especially with family (as in kids involved), you will be rarely taking public transport as like metros in India, they are always full and getting seat is a task. Hence taxi is best and only reasonably priced option.
The main allure of Dubai is due to its proximity to India, relatively very to travel (Visa etc), decently priced tickets and lots of things to see. Shopping options are numerous and electronics is highlight due to cost saving (if you actually intended to buy, I myself bought apple watch).
Tickets (for attractions) are expensive. I paid about 22K for 4 people to go to Legoland. Burj Khalifa is like 3.5K per person.
To save, you can travel in off season. In Oct too, the heat there was unbearable and all my plans to walk and use public transport fell flat due to the heat and we resorted to using taxi everywhere mostly.
To save money on hotel and eat cheap(er) and better options, I would suggest staying in Bur Dubai area. I stayed there.
Then comes shopping which has no limit. if not you, your better half may be going bonkers in certain stores. There is a store chain called "Day to Day" which sells many items and we spent like 4 hours there. It is like dmart in India with 4 floors. Then there are 1 to 10 dirham stores. Ofcourse if you want to go branded, there is Dubai Mall and plethora of other malls.