In the OP's use it would be very hard for the cable company to prove theft of service. Radio waves are hard to prove. NOW, if you run an Ethernet cable over the alley and hooked up then yes easy to prove. A Cat5e cable is good for 320 feet. You just put a RJ-45 568B jack on both ends and use the Ethernet connect cables to the routers....

At the moms house you MUST make sure she has the security set high. Then using her SSID and password you just use the amplified antenna to capture her signal.
Now at her house you may need a 'Range Extender' that linkes to her SSID and rebrodcasts a second SSID and password. That extender need to be somewhere in the middle and get good receiption from both users. LAG in PING times will not let you 'GAME' but streaming most times it works. But you will get enough delay from when you click your mouse button till the reply gets back to you....