You aren't going to be able to remote operate a cable box that way. Maybe you could kludge something to operate a wifi direct remote that way, but no chance of an IR remote (not without a lot of time on your hands and programming).
 
You might be able to do it with something like a Slingbox over wifi. I am not on the super up and up with sling boxes, but if you can pair them (which I think you can) over the network so that one slingbox is "slinging" the current channel from the cable box to the other slingbox, that'll work over the wifi connection and allow you to change channels to (I think). Then if you want it over coax, there are HDMI over coax converts, but keep in mind, this is going to be HDMI over the coax, not in a cable TV format over the coax, so you'll need another HDMI over coax coverter on the other end of the coax.
 
If what you are looking for is to basically send one channel (or worse, all of them) at a time over your wifi bridge, to your grandmother's house, covert it to coax video signals and plug it in to the back of a TV, its not going to work with any product out there.