Slide the window from side to side and see if there is excessive movement in its travel, if so the window seals are worn, worn window regulator could cause it, Realistically the door trim needs to come off and operation needs to be inspected. Checking for loose/worn/broken parts.

go to www.cadillacsonly.com...their search engine is currently being modified but you can email them and they usually get back to you within a few days of part availability

The trim panel has to be removed and rivets holding the broken handle have to be drilled out. The new handle will need to also be riveted in place. The rivets are of a specific type and size and likely only available from Cadillac . GM parts. Dorman makes a replacement handle for under $50 if bought online. The left front door part # is 80467 and the right front door is 80468. Unless you have access to a professional rivet gun that can install 1/4" diameter rivets, do not attempt this job yourself. If you will do this job yourself then you will have the repair manual in front of you that has the steps and the pictures so that you do not break any part of the trim panel when removing it as so many people do,

The system might be low on refrigerant charge.

Freon needs to be recharged

The system is low on refrigerant. add refrigerant and see if problem is resolved.

You asked and I answered. I have seen this condition many many times, only difference here is that you are mentioning the rear hot as well. Forget the rear for now. What you describe in the front, cold on pass side, hot on driver side is indicvative of a system that is low on refrigerant. The reason for the left to right difference is because the evaporator which is not fully saturated with refrigerant because the system is low has the distribution ducts aligned with the face of this evaporator and the part of the evaporator that has refrrigerant saturation is ice cold and the other part of the evaporator is not cold. The pass side ducts are aligned with the cold part and the driver side ducts are aligned with the not cold side. Attach manifold gauges and look at high and low system pressures to confirm OR just try adding more refrigerant. If you were to check pressures and found them normal then and only then would I direct you to check the driver side blend door actuator and then to start checking for a different reason that rear was blowing warm.

Turn the hot cold knob and see if you can feel a change in discharge air temperature. If you feel a temperature change then the blend door actuator is working. The blend door actuator controls that, but, and this is a big but, the blend door actuator can ONLY be a possibility if your vehicle is equipped with "dual-zone" climate control, meaning that you have a hot / cold adjustment for the driver and the pass side - individual comfort settings. Not sure if Base deville has that or not. Because one hot / cold knob cannot be responsible for two different temperatures coming out of ductwork. Only a system that is equipped with dual-zone can have a failure of a blend door actuator on one side while not affecting the other side which would have it's own blend door actuator as well.

You may try the local auto salvage sources in your area. You may also try the many on-line auto parts sources, such as; www.autopartsfair.com, www.usedpartslive.com - to name just a couple.