What if there is an executor?
This person is then responsible after the death of the testator (grandfather) to implement the last will and testament of the testator (grandfather) and to divide the inheritance and if necessary also to manage.
If the inheritance, is not Lynette's, which is probably because Neil said that Lynette was not rich, but her father who did not want to help them.
But if grandfather has a will and has named an executor (Priscilla), the executor must carry out grandfather's last will and testament. For example, if grandfather's will is that the MC should first prove himself worthy to receive the full inheritance and not just the statutory compulsory portion?
This may include so that the MC does not get the check and the package with the clothes and the diary until he is 19. Why? It may be the grandfather's will so that the MC reads something specific in his mother's diary that discredits Neil. At 19, the MC is old enough to handle something like that. But why at 19 and not at 18?
Maybe because Lynette was 19 when she delivered the MC and died.
Everything you said is legally possible and I wouldn't blame DPC for the parts that dont quite work because at that point it gets highly technical and the differences from state to state become so convoluted that, given that BAD is a pr0n game and not a law thriller, you really just have to go with the flow of the story.
You can name anyone of legal age as the executor of your will, he would then file your last will with the probate court.
The will would also overrule the normal order of inheritance.
You can also will a specific item, like our mystery box, to a specific person.
The will could also include optional terms, like "only if X finishes college and gets his/her degree will he inherit Y." (they even made a movie out of that one called "The Ultimate Gift")
The age of the MC would no longer matter, because while you can tie an inheritance to a benefactor reaching a certain age, it would most likely just be tied to when the testator died.
Where it gets tricky is the law that binds the executor, he namely has to inform all heirs, even those that were disowned in the will, of the contest period. It's a timeframe in which all legal and named heirs can accept, decline or most importantly challenge a will. Nobody could have done that for the MC, so that is where it kinda falls apart.
Right now I still favor the "someone just send the MC a box" theory. And I agree with you that one of Lynette's parents are the most likely suspects, however I wouldn't discount Neil or even Lynette herself. 18 year old girl gets knocked up, can't handle it, doesn't want to abort and the diary ends up being her confession as to why and how.
I'm 99.9% convinced that Neil knows more than he is telling, there is almost no reasonable way where he doesn't, but I fear that story will not reach a conclusion untill Season 4.