Dispute between the woman giving birth and the midwives. Who is loyal?

A mother claims that her son was born at a certain minute (when he came into the world, she looked at the clock because it was right near sunset and it was important to her to know exactly when he was born)
The midwife claims that the son was born a few minutes later (her job and duty is to be precise, as soon as he came into the world she looked at the clock and wrote down with great precision what the clock showed)
There are NFPKs of just a few minutes between them that were produced. Several NFPKs.
Like when to circumcise him (it's either 2 minutes before sunset or 3 minutes after it)
When will he be 13 years old and obligated to obey the commandments?
When will he enlist?
When will he receive an old-age pension?
And what if a woman is consecrated on the basis that she was born on the day her mother says so or the midwife says so?
 
The midwife claims that the mother, due to tension pain and the pain of childbirth (without an epidural), made a slight mistake. The woman in labor claims that it was really important to her and that the midwife is just a moving picture and accuracy is not important to her, etc.
When to meet?
According to the mother? Or according to the midwife?
And if it were to be depicted the other way around, with the midwife ahead and the mother behind? What would be the ruling?
And if it is decided (as in Figure 1) that the midwife is trustworthy and not the mother, is it up to the father and the judge to decide when to circumcise, but can she, in and of herself, or perhaps even be obligated to believe herself, take a stone and circumcise her son's foreskin?