Which is better: delaying the prayer in order to pray with a mother who sometimes delays it by an hour or two, or performing the prayer at the beginning of its prescribed time individually despite the mother's sadness due to that?

There is no harm in delaying the prayer beyond its initial time to perform it in congregation with one's mother; rather, it is preferable, both for obeying one's mother and for attaining the virtue of congregational prayer. There is no sin in this, as long as the prayer is performed before its time expires. However, if the mother delays the prayer until its legally prescribed time has passed, then this is not permissible, nor is it permissible to delay the prayer awaiting her. Instead, it must be performed at its specified time, as Allah Almighty says: "Indeed, prayer has been decreed upon the believers a time-bound ordinance."