Is relying on the hands when rising for the second rak'ah considered a pillar, the omission of which invalidates the prayer, and what is the ruling on previous prayers in which this was not done, and what is the ruling on congregational prayer at home with a parent who is unable to go to the mosque?

I misunderstood Sheikh Al-Albani's words. Standing in the described manner is not a pillar according to him or anyone else; rather, it is only a recommended act, and the prayer is not invalidated by omitting it. The Sheikh's statement, "and it is a pillar," refers to the second rak'ah. As for praying in congregation with one of the parents at home, the obligation is fulfilled, although praying in the mosque is preferable. One can combine both by praying in the mosque and then returning to pray in congregation with his parent at home.