Hi:
Here is my suggestion:
1. Get yourself an RF remote control Tx/Rx pair. For example, check this out: **broken link removed**. If you wish, you can build your own for less by using their AM transmitter, but then you will have more work to do in the signal encoding/decoding section.
2. For the Tx side, you can power the circuit from the car interior light (as soon as the interior light turns on, the Tx turns on from the same power supply. Might want to use a voltage regulator for the Tx for when the car is running (lots of noise and spikes which can kill the Tx). You might then add a two minute timer (lots of 555 based circuitry floating around).
3. For the Rx (inside your house) simply use a cheap timer from WalMart (no, I do not own WalMart stock!) and simply set it to turn on between the hours you need. When it is ON, it then powers the Rx, which will then ring your doorbell or other alarm. When the timer is OFF, the Tx can transmit all it wants, but the RX will then not be reacting since it is powered off. That way you do not need to mess with Real Time Clocks etc.
Hope this helps