@Wundy I think the public perception of any reconciliation is something BP will take into serious consideration and I would think this alone would be prevent a return to royal duties.
I don’t see that going down well with H however, given the many number of times he’s assumed something is in his fathers gift to give and resenting not getting it, when it simply is not within the purview of the Monarch (even if the “father” wished to provide it). Security is a good example of this, as is “being cut off” from the DoC funding and more recently his allegations about his children’s passports.
The only possible forward path I can see is very controlled private visits to the UK to see KC (no pictures, press and a watertight non-disclosure agreement) and if they keep their noses clean and stop leaking potentially then being able to attend some family (not official) functions - limited to family who are agreeable - at this point probably only The York’s.
Any return I imagine being carefully phased and with very clear boundaries. In time, it’s possible that their family contacts may grow if they demonstrate they can be trusted again, but my bet is that will only extend to more junior members of the family (maybe the Tindall’s or the Phillips). I can’t see William, Anne or Sophie softening their position if I’m honest.