As a GM Certified Transmission Tech, I have seen this senario in the past, the p0751 code is for the 1-2 shift solenoid. in most cases, it had shorted out, causing the plastic in it to melt and thereby sealing the vent on the solenoid, which in trn caused your hard part failure. I actually have an 08 Lucurne on my hoist right now that has done the same thing.
now the p1811 code is for the trans Pressure control Solenoid failing, these are common among the 4T65 Transmissions, but they don't cause immediate damage to a trans, when the P1811 code is set in the PCM, by default the PCM commands the trans pressures to full. there fore you may have noticed the harshness in your shifting.
I am assuming you have since had repairs done, in most cases, which GM pricing, it is usuaully cheaper for a cusmtomer who is paying out of pocket to have a SRTA unit installed, which comes with a much better warranty...