All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If your father, who is your Wali (legal guardian), had authorized your maternal uncle to act as your Wali and he conducted your marriage contract based on this authorization in the presence of the two witnesses, then the marriage is valid and there is no need to annul it in the first place. So live with your husband in kindness and repel such devilish whisperings from your mind.
We do not know what you mean exactly by saying that your father believes in democracy. However, we say that as long as the person's profession of Islam is confirmed with certainty, he cannot be declared to be a disbeliever except with certainty. There is a difference between believing in democracy in the sense that people have the right to issue legislation and govern their affairs even without the Sharee‘ah, which is disbelief, and believing in the permissibility of voting in elections in pursuit of an interest in the Sharee‘ah. Many scholars held that such voting is permissible based on the general need to defend the good against evil. If your father believes in democracy in that sense, then it is not considered disbelief. It is important to know that there are conditions governing Takfeer (declaring a Muslim individual or group to be disbelievers) as underlined in Fataawa 8106 and 87963.
As to the doubtful marriage and whether the woman should observe ‘Iddah before remarrying the same husband, scholars held different views concerning this. The answers in the two Fataawa, to which you referred in the question, are not contradictory; rather, we mentioned in one of them that some scholars held that a woman in that case is not obliged to observe ‘Iddah and that she does not need to verify that she is not pregnant. It is a strong scholarly view and there is no harm, Allaah Willing, in following it. This matter is subject to Ijtihaad (personal reasoning) given the absence of a decisive text that cannot be counterargued. Please refer to Fatwa 86301.
Allaah Knows best.