It appears that Miyagi is in Boston, attending a War Memorial service and visiting the wife of an old friend (the grandmother of Hilary Swank) and therefore doesn't have Daniel with him, nor is he anywhere near (I don't know if you know US geography, but Boston and California are on opposite sides of the country).

He mentions Daniel, though, so I don't think there's an intentional "leave Daniel out of it" effort.

The reason why Ralph Macchio didn't appear in this was because he told Columbia Pictures that he didn't want to appear in any more of these after KK3. In fact, he publically said that he didn't want to be known as the "Sylvester Stallone of Karate Kid Movies" (in reference to the series of Rocky films that were being made one after the other) and that he wasn't "interested in doing 12 sequels". He said also that he wanted to try and play different characters. He actually did that after KK2 by starring alongside Robert Deniro in a play called Cuba and his Toy Bear. He also publically said that Robert Deniro was an actor he admired greatly and always wanted to work with him.

Again, the reason described above is why he didn't appear in the NKK. Coulmbia Pictures respected that and after KK3, he was released to do whatever he wanted careerwise.

I hope that this straightens everything out. If not, then I tried.Sincerely Frank R.Schoonover