Deck has moved away from house
In all honesty, you are kind of chasing after a chimera trying to do something like that.

The likelihood is that the footings for the deck are inadequate, so that is why it is shifting. Trying to attach it to the house is not a solution. If the foundation of something is unsound, then that thing is unsound. A lot of people think they can just build decks on mud, then when bad things happen they start trying crazy stuff. Look, if the foundation of your deck is shallow, then that is your problem.

Here is the solution to your problem: build proper footings for your deck.