I'm really not an English teacher <G> but I recall my 5th (or 6th?) grade teacher saying this:
We can use 'some' if we think it's possible and 'any' if we think it's not possible.
Example:
If I ask you 'Do you want some coffee?', it means that I believe you do want coffee.
If I ask you 'Do you want any coffee?', it means that I believe you don't want coffee.
But, somehow, what you said doesn't sound right. I think even 'any' doesn't sound right.
I would try instead 'Is he going to visit any of his relatives next weekend?' or just 'Is he going to visit his relatives next weekend?'
AnnaBtG.