I've been asked to throw my two cents into this discussion because of my legal background in the CF but honestly, I have no idea which way this would go. I would think that someone from within the CF recruiting system should have encountered this before and perhaps have an internal policy instruction to rely on.
Legally there are two competing issues:
One - enrolment is a one time event and the regulations simply state that the consent is required to effect the enrolment. There is nothing in the enrolment legislation/regulations that requires that the consent to be a continuing consent.
Two - childhood (and parental authority) is a continuing event until the age majority is reached or the child becomes legally emancipated.
In my humble and very legalistic view, the consent is a one-time consent to enrolment and not required for continued service in the CF. Once freely given, and once enrolment is completed, the consent is no longer revocable and the individual remains a member. And as I've said many many times before -- I'm retired now, no longer practice law and this is therefore not a legal opinion but merely a wild a**ed educated guess.
That said, the CF is a terribly risk averse organization and would undoubtedly not wish to be involved in a hissy fit between a son and his parents.
The line that you use ". . . they have stopped me from attending training nights should I make a mistake at home . . ." makes me wonder if their position on your military service is more a manner of disciplining you for other issues rather than a fundamental disagreement with military service. Maybe I'm reading too much into that.
I agree with what most of the other folks here have said: the issue is one that you need to resolve with your parents. The chain of command is not about to take your side and tell them to get into line for you. At best your parents' threatened actions will be an embarrassment for you and at worst can lead to you being considered an administrative burden for your unit.
Best of luck.