Yeah get a bluetooth controller. I have the Madcatz Micro and it works flawlessly with my smaller hands. You can check afterpad.com for reviews on other options. Madcatz is one of his highest rated.
Get the Nimbus, it's co-developed by Apple. http://9to5mac.com/2015/10/27/hands-on-steelseries-nimbus-first-made-for-apple-tv-game-controller/ Also reading good things about the HoriPad Ultimate. http://9to5mac.com/2015/12/23/review-hori-horipad-ultimate-for-apple-tv-ios/ Stop by an Apple Store and see if they will let you hold them for comparison.
I'll add my voice to the Madcatz users, the CTRL I is a pretty good controller sporting a quite robust build. Only downside is no rechargeable battery. I must say, even though I love using touch controls (as they really add to the immersion), using a controller definitely completes the console experience for games like the newly released Assassins Creed.