IIRC, Diana wanted to console Florence's daughters which is how she ended up sitting up front or at least that was her words of why.

She also said she was too distraught and wanted to grieve privately which is why she didn't end up at the cemetery.

Her and Mary definitely should have talked before the funeral and I'm very surprised they didn't. But I think it was only appropriate they stood up at the casket together. Sad to think that the three of them were only together twice after they split, including this one time.