Alternator whine is caused by a small amount of AC signal component on your DC power supply to the radio. The alternator generates this AC signal as a by-product of how it works. A diode pack on the alternator converts AC current from it's windings into DC to charge the battery. The battery "smooths" out the pulses of energy from the alternator. For more information on this bit, see here: http://auto.howstuffworks.com/alternator3.htm.
To eliminate the alternator whine, you need to remove this AC signal from your DC supply. You mention that the whine has gotten worse, which probably corresponds to the deterioration of your vehicle battery — i.e. it is not smoothing the pulses out quite as well. This is a side issue.
The approach I would use to eliminate the whine noise, and that has worked for me before, is to run wires from the radio directly to the battery, where the smoothing should occur. Adding a filter in the supply cable, specifically the positive cured the issue for me. I used a large DC choke from an old power inverter (used for a similar job inside that) — essentially a large inductor capable of handing the current your transceiver needs — in series with the supply, followed by a large-ish capacitor (25 V, 10 000 µF) on the radio side to dissipate any noise passing through the inductor.
This worked pretty well for me. YMMV.