Salaam Ibn Sadique, habibi, hadith Saqalain is narrated in the hadtih books via different chains and is considered authentic by most if not all the Sunni ulema. If you doubt the chain from Tirmidhi then then see for example Musnad Ahmed Volume 5 has the following hadith:
Prophet muhammed (saww) said im leaving behind me two leaders the book of Allah a stretched rope in between the sky and the earth and my progeny my ahlu albayt they shall never separate untill they meet me near the the hawth"
The Prophet [sawa] said: I am leaving two weighty things, the book of Allah and my Ahlul Bayt, and they will never seperate until they reach me at the fountain.
AlHakim and Dhahabi authenticated the above. Mustadrak 3/148
The Prophet [sawa] said: I am leaving that which if you hold onto you will never go astray: the book of Allah and my Ahlul Bayt, and they will never seperate until they reach me at the fountain.
Shu'ayb Arnaut authenticated the above.
For sura Shura verse 43 you said that Allah (swt) wanted only love and care for the family of the Prophet. Is your claim backed by the Quran? The Quran clearly says:
25:57 Say: I do not ask you aught in return except that he who will, may take the way to his Lord.
and then Quran says:
42:23 Say: I do not ask of you any reward for it but love for my near relatives; and whoever earns good, We give him more of good therein; surely Allah is Forgiving, Grateful.
Loving the near relatives is related to the way to the Lord.
As for who the near relatives are, you should read tafseer of Ibn Hajr in Sawaiq on who on authority of Umar bin Khattab has said that the near ones of the Prophet are none but the Ahlul Bayt only. You could also see Tafsir Kashaf, Sahih Muslim, Musnad ibn Hanbal and Tafsir Durr al Manthur etc.
And again you said that the Ahlay Bayt include the wives which is not true. Most if not all of the major Sunni tafaseer of Quran 33:33 state who the Ahlay Bayt are and it do not include the wives.
Now very briefly, the 25:71-74 from Quran refers to the Imams of the Ahlay Bayt. Nobody but them fits the description of the leader set upon in the Quran. None of the Khulafas even from Bani Ummaya or Bani Abbas ever claimed to be the ulul Amr.
And Imams certainly could lead astray. These are the Imams not chosen by the Allah (swt) as states in the 9:12.