Nannarose
Whilst I agree with you JaneJudge, it does make sense to be careful around folk without children, as we don't know their story. Neither do we know why someone has taken on the care of an elderly relative.
But actually, OP, I can't help thinking that this is a game neither of your colleagues can win! Both are tired - do they normally get on well? I agree that a tactful word with the mum might be helpful, but she also merits some sympathy.
Yes they get on fine.
I think everyone's experience of both looking after young children, or looking after toddlers is different . I really can't agree with your post elegran. It might be your experience, and a totally valid one, but assuming that's how it is for everyone is unfair to the many people who are exh6from looking after elderly parents.