What is the ruling on praying in a masjid of the people of innovation, and where should I pray if I don’t find a masjid belonging to the People of the Sunnah in this village? Is it correct to pray in my house with my wife?
No, if there is a Masjid present (in your village) pray in it, even if it belongs to the people of innovation. Ibn Umar (radi Allahu ‘anhu) used to pray behind Najdah Al Khaarijee (the renegade), (in fact) Imaam Bukhaaree used this as a proof.
(Praying) in congregation is a great affair which is not to be left due to the likes of this. Furthermore, you have from the people of bid’ah those who do not display their bid’ah. If his bid’ah is hidden pray behind him. If it becomes manifest to you that he is an innovator, clarify the truth to him; if his bid’ah is kufriyyah (i.e. disbelief) and he remains upon it, do not pray behind him for the proofs have been established against him and he has disbelieved. This is if his bid’ah is mukaffirah (i.e. disbelief). (Bid’ah mukaffirah) is like supplicating to other than Allah, slaughtering to other than Allah, invoking upon other than Allah in times of peril, denying and negating Allah’s Attributes etc. If he has with him bid’ah mukaffirah and you have argued with him and made clear to him the truth (by presenting the proofs), the Speech of Allah, the speech of His messenger ﷺ, and the speech of the salaf and then after all that if he pompously remains upon his bid’ah, don’t pray behind him.