Those are two separate claims though. When you signed the BMW repair order, it likely limited their liability to the cost of the repair they did. They are unlikely to take on consequential liability.

You can claim against the insurance company, and say there was a problem evident during the warranty period. See what the policy says about when coverage ends, and if there is a carry over for problems diagnosed before expiry or evidenced before expiry.

But I don't see how this two way split (leaving the Mercedes dealer out for a moment) works out well for you, since BMW can refer you to the warranty company, and vice versa. You don't have a guarantee of being kept whole because it is the fault of "one of the above". I understand you bought the policy from the Mercedes dealer. So you have three parties, and if you purchase a used engine yourself you will increase that to four. Not conducive to settlements. Good luck.

__________________
2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue