Business flights to Europe with 2 separate velocity accounts

Hi team, I just need some advice on this scenario.
My wife and i are planning on flying to Europe next year with our 2 kids using our velocity points. Having done some research, i discovered its pretty much impossible to find 4 business class flights together.
I have been advised i would have more of a chance if i break it up and find 2 flights on one day and the other 2 on another. Most of the velocity points are in my account. I would buy flights for me an one of the kids using this. I was wondering am i able to buy my wife and other child flights using my points as well or do i need to be on the same booking.
My wife is a velocity member, should i just transfer her enough points to buy the second flight?