sorry to say but nope, thats why its called THIRD party only,
unless you are a NAMED driver on you bro in laws policy.
YOUR insurance ( if you are 3rd party any car ) will cover any vehicle you hit - but not the car you are driving.
and as now the case, your bro in laws company have no liablity to repair ANYTHING, ( again unless ur a named driver ) as you were driving it on your own policy.
There is nothing you can do, this is the risk you take driving like this, a mate of mine is STILL paying for the car he wrote off on this way ( his now EX girlfriend
)