You'd probably have more effect mentioning that the sensitivity training is insensitive to people whose families are abusive, especially given significant groups of minorities are disproportionately affected.
(Personally as an adult who continues to deal with difficulties regarding abusive family, I would feel highly uncomfortable with "we're a family" rhetoric- this is the exact rhetoric abusers use when abusing their family!)
If HR ever asks specific groups(as a way to dismiss you), feel free to bring up LGBTQIA+ and CSA (child sexual abuse). That tends to really light a fire under some asses.
(Personally as an adult who continues to deal with difficulties regarding abusive family, I would feel highly uncomfortable with "we're a family" rhetoric- this is the exact rhetoric abusers use when abusing their family!)