Getting pay from other firm

What is the name of your state?NY

Hi,
I've a software consulting firm through which I placed one consultant at one clients place through another consulting firm .
I've an employment agreement with that consulting firm in such a way that I've to give 30 day notice for my employee
before leaving project at clients place.
I informed the other consulting firm about my employee's exit 17 days before citing marriage as a reason.
The other consulting firm told my employee not to inform client about this and they told him that they will take care of it(informing client).
Once he left the project they told me that they are not going to pay anything because my employee didn't give 30 day notice and I can talk to their attorney.The consuling firm HR people are not available for my phone calls and not replying my emails
Immediately I checked with the client
I got a feedback from the client saying that all my employee's expenses have been approved but they are unhappy with
my employee's quick exit(other consulting firm informed them 4 days before) as they are looking for 15 days notice.

What are the best chances of getting money back from other consuling firm?

What are the best chances of getting money back from other consuling firm?

50-50

Trying to take advantage of that clause

As in this case client payed the other firm,

They are playing with that 30 day notice clause,they didn't inform me or my employee about that saying we won't pay if my employee won't stay for another 15 days.They are trying to take advantage of that clause in the agreement.