Auto Air Conditioning & Heater Repair: AC cold at idle, warm while driving, blows hot, turns off

Question
My wife's 96 or 97 Honda Civic a/c blows cold while idling, and even if while idling the engine is reved to 2000rpm still blows cold.  But while driving/moving, it blows warm and I think the compressor shuts off.  Get to a stop light, and it kicks back in and blows cold nicely.  We are in South Florida, where it is in the 90's and humid now, if that matters.  A few months a go an engine coolant hose behind the engine burst, but otherwise nothing has been done to the car since then.  Car has 175K miles.  Some kind of sensor problem?  Also, probably totally unrelated but her fuel guage sender in the gas tank is sticky but that's been going on for a while and we just haven't bothered to replace it.

Answer
As for the fuel gauge sender... take the float out of the tank and emery cloth the guides it runs on. ALOT of pain in the butt to get to it. My 99 expedition does the same, I just keep a good idea of what I have left.
Ok, now the real problem. Without your gauge readings, I am going to go as far as I can with this. If you can send me the pressure readings for your high and low sides (with A/C on, and the engine at roughly 1500 rpm) as well as the temperature around the car when you take them, I will be able to help more.
You have two pressure safety switches inside your system. One for the high pressure and one for the low pressure. The low pressure cuts off the compressor when the pressure drops below a certain point, typically between 16 and 26 psig) At idle your compressor is not turning as fast therefore your low side pressure switch stays engaged. The faster the engine revs, the faster the compressor turns therefore it is going to pull a lower pressure on your low side, and may be disengaging your switch. It is very possible that your refrigerant charge may be low due to a small leak. As the engine develops higher rpms, it pulls the low side pressure below the opening point and shuts down your compressor. With your pressure readings I can expand more, but from the sound of it this is the most likey cause. A low refrigerant charge.
The other switch, the high pressure switch, protects your system from overly high pressures. The main problem of high pressure is a dirty condensor. The condensor is located in front of your radiator. Check it to see if there are any leaves blocking airflow through it, dirt or sand in between the fins, or if more than 20% of the fins are bent/damaged. If it is dirty, a simple water hose will do wonders for it. If the fins are damaged/bent, a tool called a fin comb is available at most auto part stores and used to straighten them back out.
I hope this information helps you out. Try cleaning your condensor and if that does not help send me your pressure readings. The A/C world is controlled by pressures and you would be amazed at the different things they can tell a technician.
Thanks for your question and I await your reply with pressures.