Absolutely not forced into anything by JMB - he was not the forceful type - but possibly seduced by JMB's friendship with Capt Scott, combined with an innate desire to strike out on his own. Jack was no intellectual, nor indeed a snob, and probably found the whole Eton thing a bit of a bore.
I'm intending to post JMB's letters to Jack and Gerrie later this year, so you'll be able to judge for yourself as to what terms he was on - mostly financial I'd say, but maybe I'm being too cynical. The impression I got from Nico, and from Peter's Morgue plus the letters twixt the two, is that Jack resented Barrie's evident take-over subsequent to his parents' death, but he was too much of a realist to put up any real resistance. The fact that he always referred to JMB somewhat sardonically as "the Bart" (short for Baronet, which JMB became in 1913) says more or less everything in my view ...