my 2 cents, if your dad was not involved in the day to day running, and he didn't ask you to join the company (since you're working elsewhere), no reason you should get involved now.

how is the company's health ? as a Director / Shareholder you have full access to the Audited Reports, ask the company auditor to go through with you.

like you said, there are alot of gentleman agreements in the past. if you don't own more than 51% of the shares they could :

1. pakat to set you up. ie introduce a bad client (kickbacks) so they have something to hold against you

2. persuade you to take less of the profit (maybe saying they've worked longer and deserve it etc) this can be in monetary form or benefits like company car / house

3. ask your staff to do 3rd party work on company dime, so foc labour for them

4. waste your time with small court cases / requesting to be kept up to date on every little detail

5. bogus "agreements" that nobody knows of before this

Of course everything above is just from imagination, but I think an important question you could ask the other Directors now is what is their plans for the company. If they plan to pass to the next gen, why not involve the kids now so you can start with a fresh team while they can still provide mentorship.

If they plan to exit/sale , why not sell to you now so you're free to do as you best see fit.