I don't think that wearing pjs in public says anything about a parent, other than that they value being comfy. Pjs are lovely and life would be a lot nicer for women if we didn't feel pressured into wearing often uncomfortable clothes bras mainly and could just go with comfort.
I certainly don't think pjs = unwashed or mentally unwell. I wouldn't do it because it isn't the cultural norm where I live, but I don't see it as 'worse' than wearing joggers or leggings and both of those are acceptable in public.
As for the head, she ought to remember that she is the children's head teacher and not the parent's. It is beyond her remit to tell adults what they should and shouldn't wear.