Is a mother's prayer accepted if she closes the door on her crying child so she can concentrate on her prayer or to avoid missing its time?

There is no harm in closing the door on one's son if no harm befalls him. However, if there is a concern about the negative consequence of his crying and the worshiper becoming distracted by it, then it is preferable to give him something to keep him occupied or to place him with another member of the household. Achieving khushu' (devotional humility and concentration) in prayer is its essence and fruit. The acceptance of prayer is among the matters of the unseen. Therefore, a Muslim should strive to perfect its conditions, pillars, and obligations, along with khushu' and sincerity to Allah Almighty.