Chevy Silverado 1500 Towing Question

[B_and_D]

We towed our TM up to Yosemite last weekend. We encountered some slower moving vehicles that we got stuck behind at low speeds on steep, curvy roads, and when we tried to get around them in the passing lanes, it seemed that the transmission would try to downshift, but wouldn't stay more than one gear down. It would momentarily downshift into the 2nd gear down, but then it seemed like it was slipping, wouldn't stay down in that gear. We didn't try to use the manual downshift on the steering column.

I think the engine has plenty of power, and when we used the "tow" mode it seemed to help. Has anyone experienced this when towing uphill at slow speeds? If we were going over 35 - 40 it wasn't a problem, it just happened while we were going 20 - 30.