You miss one important detail. H&M don't want the visit to be private. They need it to be public, because their whole image depends on the royal connection. One that they have now absolutely burned to the ground.
Do you think for one second a reigning monarch can just hop on a jet to their house and hang out with the grandkids. MM will have the paps there in a heartbeat, Oprah in the back garden live streaming the whole thing, serving him jam and toast and taking pics for Instagram.
Charles has every right to choose not to have his image and his time used for promo so that the two of them can make some money. Especially after the shitstorm they brough to the Queens door when her husband was dying and she herself was in her final years.
They want public and Charles wants private. After the things they said in interviews and books about all of the senior royals, Charles does not owe them a thing.
The Royal Family are doing perfectly fine without H&M, H&M aren't doing perfectly fine without The Royal Family. This is a case of be careful who you kick on the way up because they will be there to meet you on the way down.