Eastern;
Shias do not follow the 14 personalities out of their own will. It has been commanded by Allah (swt) to follow them. As such, and I agree with you, that being a relation of the holy apostle (pbuh) in itself is not a reason to be included in the list of masumeens. This is supported by a hadith in the sunni books which goes as such:
The Messenger of Allah said: "Any relation will end on the day of Judgment except my relation. And the root (identification) of every one is his father, except the progeny of Fatimah, since I am their father and their root (identification)."
Sunni references:
Ibn al-Jawzi, al-Bayhaqi, and al-Darqunti, al-Dhahabi on the authorities of Umar Ibn al-Khattab, Ibn Abbas, Ibn Zubair, and Ibn Umar.
al-Sawa'iq al-Muhriqah, by Ibn Hajar al-Haythami, Ch. 11, section 1, p239
Similar tradition has been narrated by Abu Ya'la, al-Tabarani on the authority of Fatimah (AS) and Ibn Umar
The above precious tradition proves that, blood relationship is of little value in Islam and it will soon melt away when the day of Judgment appears. But what makes the relationship of the Prophet and his Ahlul-Bayt different than others is the qualifications and spiritual purity that they have besides their pure gene (which is also necessary).
As for the 12 imams, in the sahih sittahs, you will find several instances where our holy prophet (pbuh) has instructed us to follow them. Below, pls find some references:
The Prophet (PBUH&HF) said: "The Islamic religion will continue until the Hour (day of resurrection), having twelve Caliphs for you, all of them will be from Quraish
Sunni references:
Sahih Muslim, Arabic version, Kitab al-Imaara, 1980 Edition Pub. in Saudi Arabia, v3, p1453, Tradition #10
Sahih Muslim, English version, Chapter DCCLIV (titled: The People are subservient to the Quraish and the Caliphate is the Right of the Quraish), v3, p1010, Tradition #4483
Also :-
Sahih al-Bukhari Hadith: 9.329
Narrated Jabir Ibn Samura:
I heard the Prophet saying, "There will be twelve commanders (Amir)." He then said a sentence which I did not hear. My father said, the Prophet added, "All of them will be from Quraish
In Musnad Ahmad, the tradition is as follows:
The Prophet (PBUH&HF) said: "There shall be twelve Caliphs
for this community, all of them from Quraish."
Reference: Musnad Ahmad Ibn Hanbal, v5, p106
In Sahih Muslim, the traditions are as follows:
Narrated Jabir Ibn Samura:
The Prophet (PBUH&HF) said: "The matter (life) will not end, until it is passed by twelve Caliphs." He then whispered a sentence. I asked my father what the Prophet said. He said, the Prophet added: "All of them will be from Quraish
Sunni references:
Sahih Muslim, Arabic version, Kitab al-Imaara, 1980 Edition Pub. in Saudi Arabia, v3, p1452, Tradition #5
Sahih Muslim, English version, Chapter DCCLIV (titled: The People are subservient to the Quraish and the Caliphate is the Right of the Quraish), v3, p1009, Tradition #4477
Also Eastern, it is worth mentioning that Lady Fatimah (AS) is the only surviving child of the Messenger of Allah (PBUH&HF) who left progeny for him.
All the other children of the Prophet died in their early ages, without being able to leave an issue behind themselves.
The infidels of Hijaz (Arabia) used to dishonor the Prophet by saying that he does not have a son to preserve his generation. For that reason, Allah revealed the Chapter of "al-Kawthar":
"Lo! We have given you Abundance (i.e., a long-standing pure progeny). So pray unto your Lord, and sacrifice. Lo! It is your insulter (and not you) who is without progeny." (Quran, Chapter 108).
If I am not mistaken, the names of the other daughters that you mentioned were not the holy apostle's natural daughters, but were daughters of women that he married. Fatima Zahra, the Lady of Light, was his only daughter from Bibi Khadija.
I will not put too much info. in this post as it might get difficult to read.
Please let me know if you have questions on any specific part.