Diana was trying to protect herself by challenging the lies and getting the public on her side.
According to documentary I linked to - she was trying to get him to divorce her so she didn't lose custody of her sons like her mother did with her children (her mother was a teenage second choice bride as well) - that apparently was her very real fear and the papers started to refer to her as a bolter as they did her mother despite her mother trying to keep custody of her kids.
Her mother's entire set turned against her and her including her own mother meaning leading to her losing her custody battle.
I think it had less to do with getting the fickle public on side and point scoring with ex than it first appeared and more about making sure her long term strategy of making sure she retained some custody of her children. So I don't think she was mentally ill but determine, ruthless in pursuit of her goals and out to make the most of her life.
Diana's behaviour became "difficult" - pushing someone ( I forget who) downstairs.
Step mother - I think documentary said at time her brother was marrying and it was very tense between her Mother, who'd not long divorced second husband, and Father and Step Mother and Diana confronted step mum about refusing to talk to her Mum - and shoved her and step mum fell down flight of stairs. Lots of family and wedding tension playing into it all.
Though late in life she was said to get on better with her step Mum and at time of her death was in period of estranged from her mother.
Severe bulimia comes under mental illness for a start.
She herself admitted she had issues with bulimia while she was married - and eating disorders do come under mental health and are persistent life long disorders but I don't think it impaired her capacity in other areas of her life
At the time I thought she was generally considered to have won the PR wars the Wales waged in the papers - the downside being the continued press intrusion.
She may have started her marriage young and possibly naive but time it ended she was a grown woman capable of great PR stunts and who unlike her mother kept herself in her children's lives.