Why has the prayer for a child not been answered, despite being repeated during times when prayers are answered? And what is the way to calm oneself after becoming angry and objecting to Allah's decree?

Do not despair of your supplication being answered, for every supplication has three outcomes: either it is expedited, or it is stored for the Hereafter, or an equivalent evil is averted. Your complaining contradicts contentment with divine decree, and one of the conditions for supplication is not to rush the answer. The remedy for what you are experiencing is sincere repentance, increasing seeking forgiveness, and resolving not to return to sin. Allah forgives sins and accepts the repentance of those who repent.