Is the eldest son entitled to claim two rooms from his deceased father's house as a dowry for his wife before the inheritance is divided, given that the father did not mention this in his will?

If the heirs do not acknowledge that the two rooms are the mahr (dowry) for your brother's wife, then a mere claim is not sufficient. Rather, it must be proven with the testimony of two just male witnesses, or one just male witness and two women, or one just male witness along with the claimant's oath. Every dispute that cannot be resolved by a mere fatwa (definition) must be brought before a Sharia (definition) court.