H1 transfer while dependant H4 extension of stay still pending

[anonymususer]

Hi, I need advise on how to proceed on my case explained below:

 

My current employer has applied for extension of my H1 and extension of stay for my wife and daughter(H4 extension) in July 2015 while my family's i94 and H1 had to expire on September 30th 2015.

I waited until November but i did not get a reply on the extension, and so i applied for Premium processing and got my H1 approved in last week of November 2015.

But my dependent's H4 extension is still not approved and is in "received" status.

It has been 3 weeks that my H1 got approved and i am not sure when my dependent's H4 will be approved.

Now , i have a new offer from a different employer and i wish to transfer my H1.

 

Below are my questions:

1. Can i switch to a new employer by applying for a transfer of H1 while my dependent's H4 extension of status is still  not approved?

 

Also, the new employer confirmed that he cannot apply for H4 extension for my dependents while their existing H4 extension applications are not approved.They said that they can transfer my H1 first and apply for H4 extension for my family once their current application is approved.

 

2.I am worried that if i transfer my H1 as suggested by new employer, My current employer would cancel my Existing H1 and  my dependent's existing H4 application will be denied and they would go out of status as their i94 already expired on Sept 30th 2015.