Need for a 3rd lens??

I have been using two lens, a EF-S 17-55/2.8 IS and the EF-S 70-200/2.8 IS. So, I use the wide angle for groups/families primarily and the 70-200 for sports action, and at times T&I shoots.

I am trying to decide on another telephot lens that will fill the gap, perhaps overlap....I don't like primes!...

I wouldn't worry about trying to fill the gap between 55mm and 70mm. You've ruled out primes, so the only thing would be if you feel the need to go wider than 17mm or longer than 200mm.