What is the significance of seeing grandchildren?
Rashi: Refer to 128:6:2:1.
Radak: You will live many years.
Malbim: Also, you will strive to see that your grandchildren will be for the purpose of having Shalom in Yisrael. Your live is dedicated to the good of Yerushalayim, and you children's lives are for the good of Klal Yisrael.
What is the connection of the two halves of the verse?
Rashi: When your sons will have children, if one of them dies, his children will inherit him, and [Yibum and Chalitzah will not apply], so there will be no quarrels about Chalitzah; there will be Shalom in Yisrael.
Radak: You will live many years to see grandchildren, and to see the gathering of exiles. If the latter does not come in your lifetime, the Creator will revive you with the dead Tzadikim, and you will see Shalom on Yisrael.