What is the ruling on praying behind an Imam who pronounces some or most of the takbirat upon reaching the position [of the next rak'ah] and not during the transition? And is the disagreement among scholars a matter of doubt, necessitating obedience to parents in it, even if the unlawfulness of the action has not been definitively established?

Prayers performed behind an imam who pronounces the takbirat al-intiqal (transition takbirs) upon reaching the next pillar are valid because, according to the majority of scholars, these takbirs are a sunnah. It is also permissible for a congregant to follow an imam who adheres to a different madhhab (school of thought). Furthermore, even those Hanbalite scholars who consider the takbirat al-intiqal obligatory pardon their omission or displacement, given the difficulty of strictly adhering to their precise timing. As for obeying parents in matters deemed mushtabahat (doubtful or ambiguous), the majority of scholars oblige such obedience as long as the child does not believe these matters to be explicitly forbidden.