So is the situation regarding Jamal and Siffin the exception to the rule of fighting Ahl Al-Baghi and the people who rebel against the Imam of the Muslims?
If two parties among the Believers fall into a quarrel make ye peace between them: but if one of them transgresses beyond bounds against the other then fight ye (all) against the one that transgresses until it complies with the command of Allah; but if it complies then make peace between them with justice and be fair: for Allah loves those who are fair (and just). [49:9]
The situation was not as simple as you imagine to be, Muawiya(ra) held the view Qisas should occur in regards to killers of Uthman(ra). And the right of Qisas is in Quran.
قال الجعفي: حدثنا يعلى بن عبيد، عن أبيه، قال: جاء أبو مسلم الخولاني وأناس إلى معاوية، وقالوا: أنت تنازع عليا أم أنت مثله ؟ فقال: لا والله، إني لاعلم أنه أفضل مني وأحق بالامر مني، ولكن ألستم تعلمون أن عثمان قتل مظلوما، وأنا ابن عمه، والطالب بدمه، فائتوه، فقولوا له، فليدفع إلي قتلة عثمان، وأسلم له.
فأتوا عليا، فكلموه، فلم يدفعهم إليه
Al-Ju’fi (Yahya bin Sulaiman, from his book “Siffeen”): Ya’la bin Ubaid, from his father: Abu Muslim Al-Khawlani and a group of people entered upon Mu’awiyah, and they asked, “Do you dispute Ali? Are you his equal?” He replied, “No, I am not, and I know that he is better than me, and deserves this (khilafa) more than me, but don’t you know that Uthman was killed unjustly, and that I am his cousin, and that I ask for his blood? So go to him (Ali), and tell him to bring forth the killers of Uthman, and I will submit to him.” So, they went to Ali, and spoke to him, but he didn’t hand them (the killers).
Ofcourse, we believe that Muawiya(ra) made wrong Ijtihaad, but the issue was not as simple as you think.
I have a few more questions:
Was the obligation to obeying the Caliph not obligatory to Mu'awiyah and A'isha?
Firstly, don't equate Ayesha(ra) and Muawiya(ra). Their case was different.
You quoted this: If two parties among the Believers fall into a quarrel make
ye peace between them.......
The purpose Ayesha(ra) was coming to make peace between Muslims.
أن عائشة لما نزلت على الحوأب سمعت نباح الكلاب فقالت ما أظنني إلا راجعة سمعت رسول الله صلى الله عليه وسلم يقول لنا أيتكن ينبح عليها كلاب الحوأب فقال لها الزبير ترجعين عسى الله أن يصلح بك بين الناس
الراوي: عائشة المحدث: الهيثمي – المصدر: مجمع الزوائد – الصفحة أو الرقم: 7/237
خلاصة حكم المحدث: رجال أحمد رجال الصحيح
Aisha (RA) narrated: That when she came down to al Hawaab she heard the barking of the dogs then said: “I see myself returning after this, I heard the prophet PBUH say: ‘Then what would you (the wives of the prophet) do when you hear the barking of Al-Hawab dogs?’” Al Zubair bin al Awwam said: “You return?
maybe Allah will reconcile the people through you?”
source: Mujama’a al Zawaed 7/237.
Grading: Rijal Ahmad Rijal al SAHIH.
Ibn Hibban narrated, “Aysha wrote to Abu Mousa – and he was the governor of Kufah appointed by Ali-, “You know what happened to Uthman, and I came out to reform between people. Therefore, tell your people to stay at their house, and to be content until they get what they love i.e. the reformation of the Muslims’ matter.” [Book of the Trustworthy, by Ibn Hibban, vol.2, p.282]
Ibn Al-Emad in Shathrat Al-Thahab says, “When Ali arrived at Basrah, he went to Aysha and said, “May Allah forgive you.” She answered, “You too, I only wanted reformation.”” (Shatharat Al-Thahab, vol.1, p.42)
As for Muawiya(ra), We believe
He made a wrong ijtihad. But this became only apparent when Ali(ra) fought the Khawarij, as Prophet(saws) said, the group which will be NEAR to truth will fight them.
I left the other questions, because we believe that Muawiya(ra) was wrong.