The only videos more tedious than other people's vacations are
videos of other people's babies. (I cower at the prospect of
vacationing-baby videos.) Does your sister-in-law really imagine
a popular clamor for the newest niece pics? But while her ideas
about privacy and child-rearing differ from yours, so be it. That
is a mother's prerogative. Overprotective, perhaps, but not
unfair: her child, her rules.
In fact, her policy doesn't seem particularly extreme. She
simply declines to have her family album published publicly,
i.e., posted online. If she applied this restriction not to
YouTube but to Entertainment Weekly, nobody would bat an eye.
Perhaps she senses, with a mother's intuition, that hers is a
very private baby.
This conflict could prove more vexing when it comes to videos
that include both you and your niece. May you not document your
own life? Alas, here too the mother's wishes prevail.
But her policy is easily accommodated. As you suggest, you can
limit access to approved visitors at a Web site or, more
traditionally, disguise your niece's identity by printing the
customary black bar across her eyes, lending her an air of
criminality, quite advanced for a child her age.