When you bend the shingles from the addition onto the existing roof, the shingles will conform to the valley in such a way as to be at an angle on the existing roof.
The end of the shingle that ends on the existing roof will start on the addition.
This will result in the top (unexposed) part of the shingle to be closer to valley centerline than the exposed part, on the existing roof side.
Run your shingles from the addition onto the existing roof so that the top (unexposed) part of the shingle is no less than 12" from the centerline of the valley.
The exposed part of the shingle will be more than 12" from the centerline...
Keep your nails a minimum of 6" away from the centerline of the valley, on both sides.
I hope I described it in a way that is easy to visualize and understand.
You don't have to take off all of the shingles, just the ones that are within 2'-3' of the valley.
If you have 2 layers and the roof you have to tie into isn't very large it would be better to do the entire side.
You can just remove the top layer to tie it in but then your Ice & water shield won't be on wood on the existing roof side...
You can remove both layers within 2'-3' of the valley, install ice and water shield in the valley, remove old felt so that the Ice & water shield is directly on bare wood.
Then fill in the lower layer from the existing roof, carefully cutting them at the valley ( in such a way so that they don't go onto the addition), these going to smooth everything out and are going to be covered by the second layer.
now you filled in the gap, the second layer from the existing roof is not installed yet, it is the cut side...
Install the addition roof, valley and all.
Now it is time to install the second layer on the existing roof, proceed as described earlier.
If you choose to use unexposed metal in your valley, install Ice & water shield first then put the metal over that.
Rather labor intensive any way you look at it.