Oh, spare me the legalese. You wanna dance, let's dance.
We've got the contents of a written e-mail acknowledged by both sides vs. the conversation in an unrecorded phone call claimed by one side after the fact. You lose.
We've got an entire football season where the kid was played per the conditions of the e-mail vs. your claim that the coaches had the flexibility to do what they wanted, they simply chose not to -- until the only game where the father was unable to attend. You lose (I'm not a big believer in coincidence).
Absence of evidence is not evidence of absence. Acceptance is explicit, not implicit.
You are the one who initiated the "legalese" with the the ridiculous assertion that the children would be learning not to obey rules if the coaches violated an invalid demand. Despite your best assertion, you cannot prove acceptance of the conditions... you can only assume (and only that by basing your argument on the "trustworthiness" of individuals as subjectively determined by you). And even if they did accept, it would be invalid on its face. Better luck next time...