Crash logs aren't an area of expertise for me, but while waiting for a more knowledgeable response here is my $0.02
Running both should fine *IF* you have adequate resources (RAM, CPU, Disk I/O, etc) .... But your circa late 2013 CPU is ancient for the VERY computationally demanding of real-time video encoding. So for you, yea, running both makes no sense. BTW, Which GPU are you using, and are you using a GPU encode offload in OBS?
Starting and running Resolve, and then exiting Resolve should be fine... assuming you don't have other OS issues (like a memory leak somewhere). or corrupted memory in QuickSync or other GPU?
Simple test
- boot OS and let sit for 5-15 minutes to hit a steady state
- Check RAM usage and free memory
- Use Resolve, then exit Resolve
- Check RAM usage and free memory again. If RAM usage much higher, that may indicate a problem
check OS Processes to make sure Resolve (or related plugins?) still not running. IF you have a HDD vs SSD, Resolve shutting down may take some time. Are you allowing Resolve enough time to fully close?
Assuming a small memory leak, that in and of itself shouldn't cause OBS to crash (I wouldn't think). Though a kludgey work-around, at least faster than a reboot - Have you tried just logging off (OS User Profile) and logging back in?