Peter was hiding right along with the other disciples after the crucufixion and scoffed at Mary when she told them He has risen. Peter didn't believe her. At one point prior to His death, Jesus had to chastise the disciples for their lack of understanding re his pending death.
Well, just these citations for context of those situations you describe.
Jhn 19:26 When Jesus therefore saw his mother, and the disciple standing by, whom he loved, he saith unto his mother, Woman, behold thy son!
Luk 24:11 And their words seemed to them as idle tales, and they believed them not.
Luk 24:12 Then arose Peter, and ran unto the sepulchre; and stooping down, he beheld the linen clothes laid by themselves, and departed, wondering in himself at that which was come to pass.