Old movie about a shipwrecked father and his kids?

here's what I remember:

It's about a family, a father and at least two girls. I don't remember a son, but there might have been one.

They sing "Drunken Sailor" which even then I thought was wildly inappropriate!

There was a stowaway whom is discovered by the youngest daughter

.

The father, whom now that I think about it, kinda sucks as a dad, tells the little girl stories about stowaways being thrown over board and eaten by sharks so she keeps the boy a secret.

They're stranded on an island with bears.

They find a journal where a man who has long been dead describes being mauled.

There's a woman with them who is not the girls mother, or the man's wife.

I think at one point there's an orca harassing her in a boat, but I'm iffy on this, as there were tons of orca horror films around at the time that I might be confusing with this one.

When they're rescued the father proposes.

It might have been a made for tv movie, or straight to VHS.