Couldn't Beatrice have just lived with the family and taken care of the children, without having to marry Ludwig?
Like Maria in The Sound of Music? Can't see that happening. Also, can you imagine her (or anyone) broaching that idea to Queen Victoria?
Well, Maria wasn't actually a member of the family...
But anyway, I could see QV agreeing to such an arrangement if it were temporary (1-2 years, until Ludwig remarried) and deemed to be enough of an emergency.