It may be ethical (given the invidious position the second doctor was put in) but I’d be surprised if it were lawful.
As far as I know it’s never been decided by a court, so there’s no definitive answer.
But I’d have thought it’s strongly arguable that issuing a second recall basically just to evade the time limits in the Act would be using the power for an improper purpose and therefore unlawful. (Conceivably it might be different if the patient’s condition had, say, suddenly deteriorated at the end of the first recall period). But there are also arguments the other way. There was an interestimg discussion on here about an analogous case about section 5 a while ago: