How to control an AC motor with LOR hardware?

I would like to be able to control some small AC motors and one garage door motor on some animated props. The small motors are taken from animated reindeers. Since those are small, low amp, 110 volt, could I plug those in directly to a LOR channel without risking damaging to the controller?

I think it was DanoNJ that a while back advised me that I should use a solid state coil relay between the motor and LOR controller. Is this the type of relay that I should get for the small motors; they’re 110v, maybe drawing at most 2-3 amps (if that):
http://www.ebay.com/itm/Crydom-Solid...ht_1015wt_1121

Ok, now for my really dumb questions, assuming this is the correct relay to use. What is the correct way to wire this relay? Is the output side towards the motor and input side from the electrical power source?

The garage door motor is a ½ hp motor, 120v. The Craftsman technical service rep said it draws 5 or 6 amps. I don’t think that is correct. But if that is correct, I have a problem since the max amount of amps per channel of a CTB16 is 4 amps. My calculation is as follows:
1/2hp x 746 watts (per 1 hp)/120v = 3.1 amps
Now if my calculation is correct, I’m within the allow load the LOR controller can handle. Yea!
Since the above relay is rated at 10 amps, seems to me I should be able to use it as well; except one problem. The garage door opener has a 3-prong plug, where and how would I connect third wire, the ground? I remember my Dad used to cut the "d*mn" things off. I don’t think I want to do that.

Thanks for your help!!