The imam rushes through the prayer; can he pray at home with his sister in jamaa‘ah?
Question

                In the prayer place where I live there is a permanent imam, sometime when he is not there somone else is imam insteed of him. When he prays i dont have enough time to do al fatiha and many have complained on him, old people to, so there is no fatiha and everything else is also fast, and almost no khusho at all. only Fajr prayer is the only prayer when he is not the imam and someone else is, so that prayer can be done there.

Maghrib and isha can be done in another praying place where i live that usually has these two prayers that they pray there only and there they pray in normal speed, so i do maghrib and isha there. but duhr and asr in the prayer place with the fast imam, feels like it is no prayer and feel invalid and not right i always do my prayer again after finished praying behind the imam, sometime i fall behind in rukoo or prostration cause its to fast, so I do the prayer again and all feels very wrong.

So what im asking is can I pray duhr and asr at home with my sister instead?

I have asked my aunts husband who has studied in university of al madinah and he asked some or someone and he/they said it can be done.
Praise be to Allah.
    Firstly: 

    Praying in congregation in the mosque is obligatory for men 
    who are able to do so, according to the more correct scholarly opinion, 
    because of evidence that has been discussed previously in the answers to 
    questions no. 8918 and
    120 

    Secondly: 

    Recitation of al-Faatihah is one of the pillars or essential 
    part of the prayer for the imam, the one who is praying behind the imam and 
    the one who is praying on his own. This has been discussed previously in the 
    answer to question no. 10995 

    Reciting al-Faatihah is not waived for the one who is praying 
    behind the imam except in two cases: 

    (i)If he catches up with the imam 
    as he is bowing. In this case he should bow with him and the rak‘ah will 
    count for him, even if he did not recite al-Faatihah

    (ii)If he joins the imam in the 
    prayer just before he bows (rukoo‘) and he is not able to complete 
    al-Faatihah. In this case he should bow with him and not complete 
    al-Faatihah, and the rak‘ah will count for him.

    Thirdly: 

    You should try hard with the people at the mosque to advise 
    the imam to slow down in his prayer and not rush. If the imam bows before 
    you have completed al-Faatihah, it is permissible to you to complete it even 
    if that will make you delay bowing, then you can follow him. But you should 
    recite al-Faatihah more quickly, without taking your time. Some people are 
    not able to recite al-Faatihah behind the imam for that reason. 

    Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was 
    asked: What is the ruling on a man who offers a four-rak‘ah prayer with a 
    congregation from the beginning of the prayer, then when the imam says the 
    salaam, this man stands up and does a fifth rak‘ah. When the imam asked him 
    about that he said: In the second rak‘ah I was not able to recite 
    al-Faatihah so I did this rak‘ah to make up for it? 

    He replied: This is correct, but what would have been better 
    than that is if, when he stood up and the imam bowed before he was able to 
    complete al-Faatihah, he had completed al-Faatihah and followed the imam, 
    even if the imam had already stood up from bowing. 

    End quote from Majmoo‘ Fataawa Ibn ‘Uthaymeen, 13/134 

    We do not think you should stop attending the mosque or 
    repeat the prayer; rather you should pray with the imam so long as his 
    prayer is correct, and try hard to do what you are obliged to do, even if 
    you fall behind in following him, whilst continuing to advise him in a 
    suitable manner. 

    And Allah knows best.