Diana must play the part, at least, of a grieving widow. She suffered from depression IIRC, though granted this could be me remembering how she appeared becasue of the marital tumult. If it was somethign worse but just never really got discussed OTL, it may be allowed to leak out as a way to show how hard it is for her to deal with the death, even if it isn't related.
Her relationship with the rest of the Royal Family will be quite congenial for a while, at least. I think the Queen mother is still around - she will be seen as a similar persona, someone who will one day be the elderly mother who watches as her lovely firstborn takes the throne as William V. How the royal children are raised may or may not be impacted, I'm not sure. But, not only is her love relationship post-divorce butterflied away, I wonder if she would even be doing a lot of the social causes that she did OTL, at least for a while? And, will she tend to remain closer to home even wiafterward? I imagine she will still travel a lot, because she did take the place of the Queen at of events OTL, but here's where I'm not really sure how royal family structure nd planning work.