If the trailer brakes are adjusted and in good shape you should not have a big problem. My suggestion is service the brakes repack bearing with synthetic grease (higher pour point), replace brake linings and adjust correctly.
We did a trip to a family gathering a couple of years ago and came back through Yosemite and up over Tioga pass. If I remember correctly it drops about 6,000 feet in fairly a short distance and the brakes on our TV were smoking by the time we stopped for gas, carefully. You do NOT want to stop with what can be cherry red brake rotors or you can genuinely warp them when the pads do not allow that section of the rotor to cool at the same rate. The major passes on I80... are gentile enough to not be a problem.