All three verses that list the sons of David and Bathsheba list Solomon as the last of the four and Nathan third. 2 Samuel 5:14, 1 Chronicles 3:5 and 1 Chronicles 14:4.
"And these were born unto him in Jerusalem; Shimea, and Shobab, and Nathan, and Solomon, four, of Bathshua the daughter of Ammiel:"Also I don't believe the four listed here are only the "surviving" ones, I think even the one that died at birth was given a name, and that name was Shimea.
Among the things said by Critics to attack the idea that Jesus had claim to the Throne of David from Luke's genealogy is that the Throne could only be inherited through Solomon. Solomon is relevant to II Samuel 7 because he is the near fulfillment, but nothing in Scripture says the Messiah must be descended from Solomon.
On top of that go back to the account of the division of The Kingdom in I Kings 11. It says Solomon's sons will never rule a United Kingdom, only Judah. The Messiah will rule all of Israel. Meanwhile Zachariah 12:12 makes a reference to the House of Nathan that is interesting. And 2 Kings 23:11 has a mysterious reference to a "Chamber of Nathan-Melech" Melech meaning King.