This question doesn’t have a brief answer. Please click on the detailed answer.
This question is in reality divided into two segments:
1. The first is that who, from the perspective of the Shias, does the Holy Quran specify when it speaks of the ‘Ahlul Bait’. Also, are the wives of the Holy Prophet (s) considered as part of this group?
2. The second question is whether the absence of the names of the Shia Imams (a) in the books considered reliable by the ‘Ahlul Sunnah’ weakens their positions as imams? The answer to the first segment of the question has been answered in the following questions: 834 (site 903).
In respect to the second segment of your question, ponder on this example: Imagine that someone has taken a decision to go on a trip and in regards to the city of destination they have a doubt. It is natural that in such a case the individual, in order to make a better decision, will ask informed individuals as well as study maps and travel guides of various cities. He will do all of this in order to find out which city is the most appropriate and select that city.
With this said, the question is whether after we have entered our city of destination do we still have a need for the maps of the other cities that we were researching earlier and decided not to travel to? If we were to try to find a street name in the map of a city which we were not in, would we have any right to become surprised when we are not able to find it? It’s certain that you will give a negative response to this question! When we have entered a certain city, then the roads and streets that exist there can only be found by searching the correct map of that very city. Now we will return to the question that was at hand.
The Shias, in order to select the correct pathway, studied the books of both the Shia and Sunnis and after doing their research have found that even in the books of the Ahlul Sunnah the Holy Prophet (s), in various speeches, selected Amirul Mumineen Ali ibn Abi Talib (a) as the Caliph that was to come after him. This is clearly seen in traditions such as the tradition of Thaqalain which expounds on the idea that the only correct path of Islam is possible through following the Holy Quran and the ‘Ahlul Bait’ (a)  . After this the Shias don’t see the need for finding the names of their Imams (a) in certain books or for proving their jurisprudential, ethical, or political rules… There is no need to set up the reliable books of the Ahlus Sunnat as documentation for the beliefs of the Shia and in the event of not finding anything, falling into doubt due to it. Of course it’s possible to research secondary viewpoints and matters through these sources and consider them as documentation for these matters. Except in matters of finding that primary path, that we spoke about earlier (which needs varying viewpoints and sources), there is no need after that primary path is found for the Shia to prove their ideology and jurisprudential laws based on the books of the Ahlul Sunnah. The Shia use the rich resources that they have at their disposal and the lack of finding the names of their Imams (a) as being called Imams (a) in the books of the Ahlul Sunnah will not really cause any doubts or other issues to crop up.