I am kinda confused on his question. Just to clarify, - you are currently working here on working visa - and you have found a new job right? you want to transfer to that new company and have been given NOC by your previous company. your family (wife and kids) are under your sponsor, correct? then your case is simple. below example as I have done the same recently:
1. Give Computer card of new employer to old employer - old employer mandoob will prepare documents with NOC and go to immigration services. (this will take 1 to 3 days, depends on how reliable your mandoob, in my case it only took 1 day)
2. after processing, mandoob will give you back the same paper he processed (attached noc with it) and you need to give it to your new sponsor mandoob so he can do transfer of working visa to new company.
3. if your wife and kids are under your sponsor, you do not need to do anything with it - in their system (immigration) the only one needs to update is your working visa to a new company - with regards to other visas attached to you, there is no concern as it will automatically update on their system.
YOU DO NOT NEED TO EXIT. hope this is clear.