My experience is that if your M life room cost is $0 + Resort fee, it won't count for a Hyatt night credit.

If your room cost is $1 or above + Resort fee, it WILL count for a Hyatt night credit.

There is no such thing as picking where you want to "credit your stay". It always credits to M life. You just get to decide if you want it to ALSO credit to Hyatt (points plus elite night credit).