Can a levirate marriage yield a legitimate heir to the throne?

Question

If a king dies, and his brother lives, can his brother marry the dead king's wife to raise an heir to the throne? Or would a new line of kings begin?

Deuteronomy 25:5-6

כִּי-יֵשְׁבוּ אַחִים יַחְדָּו, וּמֵת אַחַד מֵהֶם וּבֵן אֵין-לוֹ--לֹא-תִהְיֶה אֵשֶׁת-הַמֵּת הַחוּצָה, לְאִישׁ זָר: יְבָמָהּ יָבֹא עָלֶיהָ, וּלְקָחָהּ לוֹ לְאִשָּׁה וְיִבְּמָהּ. 5 If brethren dwell together, and one of them die, and have no child, the wife of the dead shall not be married abroad unto one not of his kin; her husband's brother shall go in unto her, and take her to him to wife, and perform the duty of a husband's brother unto her. ו וְהָיָה, הַבְּכוֹר אֲשֶׁר תֵּלֵד--יָקוּם, עַל-שֵׁם אָחִיו הַמֵּת; וְלֹא-יִמָּחֶה שְׁמוֹ, מִיִּשְׂרָאֵל. 6 And it shall be, that the first-born that she beareth shall succeed in the name of his brother that is dead, that his name be not blotted out of Israel. ז וְאִם-לֹא יַחְפֹּץ הָאִישׁ, לָקַחַת אֶת-יְבִמְתּוֹ; וְעָלְתָה יְבִמְתּוֹ הַשַּׁעְרָה אֶל-הַזְּקֵנִים, וְאָמְרָה מֵאֵן יְבָמִי לְהָקִים לְאָחִיו שֵׁם בְּיִשְׂרָאֵל--לֹא אָבָה, יַבְּמִי. 7 And if the man like not to take his brother's wife, then his brother's wife shall go up to the gate unto the elders, and say: 'My husband's brother refuseth to raise up unto his brother a name in Israel; he will not perform the duty of a husband's brother unto me.'

Genesis 38:8-9

וַיֹּאמֶר יְהוּדָה לְאוֹנָן, בֹּא אֶל-אֵשֶׁת אָחִיךָ וְיַבֵּם אֹתָהּ; וְהָקֵם זֶרַע, לְאָחִיךָ. 8 And Judah said unto Onan: 'Go in unto thy brother's wife, and perform the duty of a husband's brother unto her, and raise up seed to thy brother.' ט וַיֵּדַע אוֹנָן, כִּי לֹּא לוֹ יִהְיֶה הַזָּרַע; וְהָיָה אִם-בָּא אֶל-אֵשֶׁת אָחִיו, וְשִׁחֵת אַרְצָה, לְבִלְתִּי נְתָן-זֶרַע, לְאָחִיו. 9 And Onan knew that the seed would not be his; and it came to pass when he went in unto his brother's wife, that he spilled it on the ground, lest he should give seed to his brother.

Answer 1

1. Kinghood is considered an asset, as is any role of authority, thus the rules of inheritance apply.
2. A brother who takes his dead brothers childless wife inherits all his assets.
3. So in this case the brother will become king (if he is suitable) and when he dies the throne would go to one of his children - that includes children he had with the former queen.

Answer 2

Mishna in Sanhedrin 2, 2:

The king may neither judge nor be judged, testify nor be testified against. he may not perform halizah nor may it be performed to his wife. he may not perform yibbum, nor may it be performed to his wife. R' judah said: if he wishes to perform halizah or yibbum, he shall be remembered for good. but they [the rabbis] said: [even if he wishes] he is not listened to; nor may any one marry his widow. R' judah said: a king may marry a king's widow, for so we find in the case of david who married the widow of saul, as it is written, and I gave thee thy master's house and thy master's wives into thy bosom.

According to Rambam, it is obviously prohibited (we do not follow the opinion of Rabbi Yehuda). According to Rashi too it seems to be a disgrace, to work for another indeed that he was also king. Note. The verse regarding Onan is not congruent with the definition of Yibum after Matan Torah.