I presume you are asking about Vishnu (or Vaishnavite) idols co-existing with Lord Shiva idols.
There are two divya desams located within shiva temple.
Lord Govindaraja Perumal is within the famous Chidambaram temple.
The other divya desam located within a Lord Shiva temple is Nilathingal Thundam Perumal. In the former temple, the worship is carried out by Vaishnavites and it is by the Saivites in the latter. Thus, the sanctity of Vaishnavite idols co-located in temples where Siva is the main deity is maintained by these priests and they are divya desams ! There is also said to be a third divya desam located within the Kamakshi temple in Kanchipuram.
All the vaishnavite temples are constructed according to either Pancharatra Agama aor Vaikhanasa Agama. Therefore, every Vishnu temple is based on the rules given above. Pancharatra Agamas alone has 108 samhita and each temple comes under a particular samhita.
Sri Ranganatha Swamy temple - Sri Paramesvara Samhita Sri Melukote
Cheluva Narayana Swamy - Sri Ishvara Samhita Sri Kanchipuram
Varadaraja Swamy temple - Sri Jayakhya Samhita Aravamudhan
Sarnagapani in Kumbakonam - Sriprasna samhita
None of these samhita discuss about placing a shiva linga within the premises of the vaishnavite temple. Therefore, the question of co-existence does not come. As Shiva agamas allows for Vishnu idols to be installed in the temple, the co-existence comes only for Shiva temples.
However, there are two famous temples that were converted from Shiva temples to Vishnu temples by Saint Ramanuja.
Kurmanathaswamy temple, Srikurmam, is one of the few temples which was assumed to be a shiva temple and called Kurmeswara temple. Sri Ramanuja converted it to a vaishnavite temple and installed another dhvajasthamba in addition to the existing one. The temples follow both the Shaivate and Vaishnavite tradition for worship.
The Varaha Lakshmi Narayana temple of Simhachalam is another temple which was converted from a shiva temple to the vaishnavite temple. Simhachalam's deity was believed to be Shiva as a linga due to the unusual position of the deity's idol. Ramanuja argued that the idol of Varaha Narasimha is in a posture in accordance with the Pancharatra Agama. Though it is a Vaishnavite temple, it is worshipped in a linga form by smartha brahmins (and not vaishnavites) for 364 days in a year. On the day of Akasya trithiya, the sandalwood paste, covering the main diety throughout the year in the form of a linga is removed. As a result, devotees can see the original form of the deity's idol for 12 hours once in the whole year.