OP shouldn't be a problem at all. I have some of the most bizarre routings and my bags made it fine.
One time I had to go to Daytona Beach and CO routed me DAL-IAH-LAX-EWR-DAB. And on the return DAB-EWR-SFO-IAH-DAL. Both LAX and SFO were CO outstations at the time. I even stayed 24 hours in SFO and they held the bag. Come to think of it I have a lot of third cities where I connect 24 hours and they keep the bag. Also no problems international. Did DAL-IAH-NRT-GUM-NAN (nadi Fiji) and NAN-HNL-LAX-IAH-DAL. Both HNL and LAX were out stations on return. Bags and flights were fine. These are just two routes. I have many!