What should the questioner and her mother do to compensate for the Hajj Sa'i they missed out of ignorance, and do they have to repeat the Tawaf and Sa'i with the intention of completing the ritual, then enter into Ihram for this year's Hajj on behalf of her deceased father and grandmother?

The pilgrim must learn the rulings of Hajj, and ignorance is not an excuse. Sa'i (the ritual circumambulation between Safa and Marwah) is a pillar of Hajj according to the majority of scholars; Hajj is not valid without it and cannot be compensated for by an animal sacrifice (dam). The Mutamatti' (one performing Hajj al-Tamattu') is required to perform two Sa'i rituals, according to the majority of scholars. Since you did not perform Sa'i, your Hajj is incomplete, and you have not performed the second liberation (tahallul al-thani).

You must return to Makkah. If sexual intercourse occurred during those years, Hajj is not invalidated, but the state of ihram is. Therefore, you must enter ihram from the miqat, and upon reaching Makkah, perform tawaf and sa'i to be liberated from the first Hajj. You also owe a fidyah (expiation) for the sexual intercourse (a sheep to be sacrificed in Makkah, or feeding six needy people, or fasting three days). Then, you should enter ihram for this year's Hajj on the 8th day of Dhul-Hijjah. You are permitted to perform Umrah before that to make your Hajj Tamattu'.