I think its pointless comparing Charles parenting skills to the average father. Charles himself was brought up by nannies and governesses. His mother was absent for large parts of his childhood especially during his formative years- he was born in 1948 and between 1949 and 1951, the queen lived in Malta while he was in the UK. She went on tours for months and months on end while he was at home. He's hardly going to be hands on, traditional father when he's had no blueprint for this himself. The royals simply dont operate the way we do as a family.
Even Diana for all her hugging in public was hardly mother of the year. She largely delegated childcare to nannies, sent both boys to boarding school at 8 and again went on lengthy foreign trips while her children were at home.
It's completely beside the point all these people saying "nothing would stop me seeing my grandchildren" and "why can't he just hop on a plane". Your average grandparent isn't a head of state let alone someone going through cancer treatment. "Hopping on a plane" as king involves high level of security planning across countries, the organisation of security staff, accommodation, flights etc. He isn't you and me. He can't just take himself off to Heathrow when he fancies and hope on the next jet to LA.
Royals dont live like we do. Everything is organised meticulously. It's the same for security. Prince Harry has his own security. He doesn't need it paid for. What he wants is tax payer funded Met office security 24/7 and it doesn't matter how rich Charles is, police officers aren't for sale. They can't be paid for by the King, or Harry or anyone no matter how much they want it.