I agree with IrishJetDriver's advice that you should take a parent along on FTO visits.
As for his advice to take mummy and daddy along during any pre-entry assessment; it appears he didn't read your post very well. I don't know of a modular course anywhere in the UK that requires assessment for modular students.
If you decide to apply to an integrated course, taking mum and dad to the assessment might create the impression that you are not mature enough to assess risk and make important decisions on your own. If you lack the maturity to go through selection testing on your own, I would say this is not the career for you.
As for the open day issue, why not just visit during the week? If an FTO can't shine in a one-on-three visit with you and your parents, then you shouldn't go there anyway. Don't go to an integrated course open day if you have already decided to train on the modular route.