If DPS is working in rural areas they communicate with Houston DPS. However inside a city they may contact that cities dispatch for warrants information or to request a wrecker .
Just last week I heard DPS talking to the Texas city PD dispatcher on Texas city PD channel one requesting a wrecker. As you may be aware Texas city PD moved there dispatch ops to Texas city PD channel two and now use encryption ! However Texas city PD channel one is used for outside agencies to talk directly to the dispatcher.
I don't know why they don't talk much on GCSO channels it is possible they could conduct operations with them on one of the GCSO events channels events A, B, C, D, Or E. I do hear DPS on these channels occasionally