Depends on the child - some would behave themselves, some wouldn't. DSS1 would be fine, DSS2 would not, lol. And there isn't much of an age gap - they just have very different personalities. I would have told the child and receptionist where I was going and where to find me if need be. However, if I was very upset about bad medical news I might not be thinking straight and neglect to do this.
The mother might not have anyone that she can lean on to babysit. As others have said - going to the GP can be very important and is very different to getting ones hair done.