U-Verse TV while keeping Cox internet?

Does anyone know if this is possible?  I've had U-Verse TV in the past and it was GREAT but ATT's internet speed was really lacking with what we needed.  So, hubby wanted us to switch to Cox.  So, we did.  And I've had nothing but trouble with the whole home DVR set up, as in, it doesn't work at all. I had 2 technicians out and they can't figure out the problem, let alone get it fixed.  We'd love to switch back to U-Verse for TV but keep Cox for the high-speed internet (the hubby uses for gaming and I use for streaming).  What I'm wondering is, is it even possible to get U-Verse TV on another separate line into your house?