What is the comparison of your wife to a fruitful vine?
Rashi: She will have many children.
Radak: A vine is the only tree that people plant in the house. When it grows, they take the branches outside to be in the sun, but the roots are in the house. So he commands his wife to be modest in the corners of the house, and not go outside. Going out is the way of an adulteress - 'Pa'am ba'Chutz 'Pa'am ba'Rechovos" (Mishlei 7:12).
Why does it say "b'Yarkesei Veisecha"?
Radak: She should be modest also in the house and not sit in the opening, where passersby will see her. An evil woman does so - "v'Yashvah l'Pesach Beisah" (Mishlei 9:14). Rather, she is always b'Yarkesei (in the sides of) your house. Only her husband and household see her. However, her sons go outside to their work, and for the sake of the house, just like the vine branches go out of the house in order to multiply via the sun - "mi'Meged Tevu'os Shemesh" (Devarim 33:14).
Malbim: Even though it stands in the side of the house, it sends its branches and tendrils on the roof and from there it covers the entire house. So she is modest and dwells in a tent in the sides of the house, and even so she guards and covers the entire house.
What is the comparison of your children to olive saplings?
Rashi, from Yerushalmi Kil'ayim 1:7: Just like there is no grafting of olives 1 , there will be no Pesul (disqualification) in your children.
Radak: (a) The saplings are good, and like their 'fathers'. So children born from this modest woman (refer to 128:3:1:2, 128:3:2:1), there is no concern for Mamzerus in them; she was intimate only with her husband. (b) Olive leaves are green and moist the entire year. So your children will be in their beauty and good deeds.
Malbim: Olives give oil for light. So they will be seed of Emes that enlighten with knowledge.
Radak: If one tries to graft another tree on it, it will not work.
Why does it say "Saviv l'Shulchanecha"?
Radak: They will be in front of you to serve you at the time you eat. They will eat and drink only on your table. They will not be sent away and gluttonous. They will eat and drink only on your table. They will not be abandoned, gluttons or drunkards. They will eat and drink only on your table.