"My DFIL was a** traditional sort, and DH just feels strongly that he would not have wanted his earthly remains split up in this way."
So he does not know for sure what his father would have wanted, I know you said scattered but would taking some out be such a terrible thing?
"It's not that he feels he owns his DF's ashes at all."
Who gets to decide, is one of them the person who has been put in charge of arranging the funeral or are they meant to do this together?
" He just wants to do the right thing by his DF. He adored him." That is understandable. Do you feel your SIL did not love her dad or did not love her dad as much as your dh?
I've had to go to two significant cremations; my dad, 12 years ago, and my mum last year. Twelve years ago there was a power cut at the crematorium when we came to scatter ashes and the staff were at 6s and 7s. A man in overalls dumped my dad's ashed on the grass, did a little bow and was gone.
My mum's was last year, my sister and I rode a golf buddy type thing to the same spot in the crematorium where a dapper little man asked us if we would like to scatter the, ashes; we did. I said to my sister "I'm not going to cry." And promptly began to cry!
It's all so personal and I would just say that the danger is for a family disagreement at this sad time (which I can almost guarantee your FIL would not want!).
*Despite what I posted a minutes ago!" I would say if your SIL has a supportive partner then I would be tempted to stick by my dh and back him up as much as you feel able to. If your SIL has a partner who takes a back seat or if she is single, I would take a back seat.
It really is between the two (or more?) siblings.
I tend to agree with CrazyCavalierLady "How people deal with their loved ones passing is personal. What the dead thought is irrelevant. They are gone. He was cremated and can still have his ashes scattered as per his request."