What is the ruling on praying behind an Imam who intentionally mispronounces while reciting, even though he is capable of correct pronunciation, and is it better to pray alone at home or to continue praying behind him?

If the Imam makes an error in reciting Al-Fatiha that does not alter the meaning, then your prayer behind him is valid. However, if the error changes the meaning (such as pronouncing the letter "ta" in "an'amta" with a kasra or damma instead of a fatha), then following him is invalid, and he must be replaced. If he is not replaced, then pray in your home, and you are not obliged to go to another mosque due to the long distance. An intentional error invalidates the prayer, even if it is not in Al-Fatiha.