I think Diana and Charles were both Disney parents in their way. Charles with the traditional aristo pursuits - huntin, shootin, fishin, polo, skiing, hiking etc. Diana with the 80s vibe of celebrity culture - pop concerts, pop stars, film premieres, Hollywood A-listers, big matches, sports stars plus some charity work etc. Then I think book were happy to hand over to the nanny (although Diana was jealous if the nanny got close). Then it was off to full boarding at age 8.
William had far too much responsibility heaped on him. Charles expected William to look after Harry emotionally and "include" him in everything. Diana used William as a confidante for her love life (and to pass tissues under the bathroom door when she was heartbroken). William was also used as her wingman when she went to meet business contacts. Can you imagine taking your child to meet Piers Morgan when he was 13 or 14? I think it explains a lot about the current Wales parenting that their children are kept out of the tabloids apart from a few official photos.
I do think Diana loved her children very much, but I don't think she really did the drudgery parts of parenting. In fact something William said as an adult made me think. She clearly used to love being the "fun" parent - she'd arrive and enjoy getting everyone hyped up and creating chaos and then she'd just leave - and leave the staff to deal with the fallout and mess.
I would guess that Harry parents the same way - he likes playing, running around and doing the fun things (as he attempts when he meets kids) - but I don't see him cleaning up the mess he creates.