OK, your first order of business is to figure out how strong a motor you will need to open and close the door. I guess you will need the door, too. I'd look for a DC motor. You can test it out without any circuitry - just apply voltage one way to open, reverse the terminals to close.
Once you know the motor, then you can do the motor controller. There is a recent thread on relay based bidirectional control of DC motors. You will also need to build the power supply. You could use an HBridge but I'm not sure how cost effective it would be compared to a relay (which is pretty cheap).
next, you will need 2 limit sensors. one for open and one for closed so you know when to stop the motor. You can use microswitches, hall effect devices or opto interruptors. I'd probably use optos. These are devices with an LED and phototransistor with a slot between them. Insert an opaque object in the slot and the PT stops conducting. very easy to interface to your picaxe. when you get to this point, ask... I'd get that working next.
Finally, get the pressure pads working. Not sure how this works but I suspect it's based either on switch closure or resitance decrease. in either case it's pretty easy to interface to a PIC. By the way, the conductive foam that ICs get shipped with might work for this. I just did a little test and the piece I had went for 8K ohms uncompressed to around 1.8K compressed. put it between two metal plates and you can use the resistance to determine if there is pressure on the pad. I don't know if it will last very long, though.
I would also build in some sort of safety interlock that will reverses or stops the door if something gets in the way while it's closing.
On your picaxe, you will need at least 5 inputs and 2 outputs.