New Circuit for 1.5HP Pool Motor
Right off the bat, finish with your original intent, and hook the cable up to a GFCI receptacle that is inside the garage.  Now come off the receptacle's LOAD terminals to your underground line to the pool area. 

What you don't want to do is bring unprotected 120VAC out to a pool area and then fit a GFCI recep there. Because then, the wiring does not have GFCI protection, and the wiring can electrify the ground.  Especially if NM cable is used, which is not made for outdoor use.  

Anyway, continue off the GFCI's load terminals via UF-B cable buried with 12" of cover because it's GFCI protected... or run a conduit type of your choice from that indoor recep outside, then switch to 1/2" Rigid conduit for the underground run to the pool, this can be buried at 6" of cover (but it's expensive).  Use THHN individual wires inside the Rigid conduit, do not put UF-B cable in conduit (won't fit anyway). 

Use 12 AWG wire or cable.  

As far as extending off the 15A circuit, yeah, you kind of painted yourself into a corner on that.  I'd go ahead and replace that #14 run with #12 (or just run it alongside) and call it a life-lesson learned.  

Violating the installation instructions is a bad idea.  If anyone gets hurt at your pool (and electrical drownings are absolutely horrible, gut-wrenching, life-changing things), they will go over your setup with a fine-tooth comb.  Any violations, you'll have a problem.