I don't know if I am a very knowledgeable expert, but you can certainly do this.
You would need an external power source for the servos, and use a relay to switch them on and off.
Here is an example on how to use relays. http://www.oomlout.com/oom.php/products/ardx/circ-11
You could hook up a single trimpot to an analog line, and when any button is pushed you can activate the relay for X amount of time where X is some scaled value of the trimpot reading.
Here is an example on how to use trimpots. http://www.oomlout.com/oom.php/products/ardx/circ-08
Finally I would use a couple of xbees to communicate between the two Arduinos. 30 yards is too far for wired, but the cheapest xbees have a 90 meter range under optimal conditions which is well over your requirement of 30 yards. This will be the most difficult part but I'm sure the information is out there on the internet somewhere.
Good luck!