What is the ruling on Salat al-Istikhara regarding procreation with one's wife, and should it be performed to دفع (avert/repel) potential problems that may arise with the presence of children?

There is no objection to artificial insemination between spouses when needed, and there is no impediment to performing الاستخارة (seeking guidance from Allah) before proceeding with it. This is because الاستخارة is prescribed when one is hesitant between performing a permissible act or refraining from it. Then, one should proceed with what their heart feels inclined towards.