Is it permissible to switch from one jurisprudential opinion to another merely out of need, while believing the latter to be invalid? And is this what Abu Hanifa did in the issue of the mouse? What are the controls for switching between jurisprudential opinions?

That by which Allah is worshipped by His servants is His Book and the Sunnah of His Prophet, peace and blessings be upon him. The jurisprudential schools of thought are merely schools for dealing with the texts of revelation and deriving rulings. The sayings of the Imams are mere ijtihad (independent reasoning), and there is no harm in acting upon one of them when necessary. Indeed, Abu Yusuf prayed behind Malik despite their differing madhhabs (schools of thought), and the Companions and Successors prayed behind one another despite their differences in some subsidiary rulings. It is permissible for a muqallid (follower of a madhhab) to depart from acting upon the well-known opinion to acting upon the anomalous one that contains a concession, as long as that is not following caprice. One must act upon the sound, definitive evidence that is not contradicted by similar evidence.