Salam
When it comes to Shia-Sunni, it is obvious Sunnis do have hadiths to support their creed in their own sources. What Shias argue is that they also have hadiths that prove Shiism and refute Sunnism in Sunni sources.
Hadeeth are classified into Sahih, Daef, etc. So may be the daef the unreliable ones refute Sunnism, as usually the case when the hadeeths used by Shias are verified. Or in few odd cases the hadeeth themselves are vague and not Qati(categorical) and explicit, and they are open for interpretation, BUT in this case SUnnis have many Qati and Authentic ahadeeth which refute the Shia interpretations to those vague hadeeths.
Now when it comes to the verse 37:130 it has been passed with two recitations in Sunni sources. One is that it's El Yaseen , or Elyaseen (referring to Elyas) and another is that it's "Auli Yaseen".
Sunnis believe all recitations are from God and even different meanings are intended to be a feature of the book.
The Surah before 37, is called Suratal Yaseen and in there, "Yaseen" is addressed with similar way the some Prophets are mentioned in Suratal Saffat (37).
It's too much of a flow with respect to the Surah before, to dismiss the relationship with it.
Now if Sunni view is right, that both, recitations are from God, then it would mean God blessing Elyas implies that God should bless the family of Yasin and blessing the family of Yasin implies that Elyas should be blessed.
So in this way the family of Mohammad are in Quran.
The flow with how the chosen ones are being singled out, implies the family of Yaseen are such chosen ones.
So this would mean that family of Mohammad are chosen guides.
Shia tafseer[The Light of The Holy Qur’an] for the verse 130 of Surat as-Saffat states:We must learn from Allah (s.w.t.) how to greet to Divine prophets, the great friends of Allah. This verse says: {“Peace be on ’Ilyāsin (Elyās).”}The application of the term ’Ilyāsīn instead of Elyās is either for the sake that ’Ilyāsīn was a word inside the term Elyās and both of them have the same meaning; or it refers to Elyās and his followers which has been used in this total form.
(Source: The Light of The Holy Qur’an by Ayatullah Sayyid Kamal Faghih Imani and A Group of Muslim Scholars, under explanation of verse, 37:130)
Comment: Interestingly we find that the Shia scholars gave two opinions, the second opinion is that Ilyas and HIS FOLLOWERS were ment by ‘il Yasin’.
Even the famous Shia translator of Quran in English language – Muhammad Sarwar – translated this verse as:
Peace be with the followers of Elias. (Quran 37:130).
I suggest you to read this article:
https://youpuncturedtheark.wordpress.com/2012/05/23/salawat-series-the-fact-about-salawatdurood-regarding-which-shias-are-unaware/