The story certainly can be embellished ...
For me, it's not an accusation thing, neither to you, nor to Sarah, or Hagar.
Sari chose to fulfill the promise by the sweat of her brow (in picture), and received the harvest she sowed, just as Hagar had of Sari.
If you believe Sarah was jovial in an honest way about it, all well and good (I'm not saying your wrong), but Sarah lied about being honest (becoming afraid after the Lord questioned Abraham over it; the Lord taking It (according to his words), as if it were an accusation against his ability to accomplish what he set out to do, and this he reminded her of before two men depart).
In the end, it's really not about Sarah or Hagar, it is about the process that leads to an only begotten son.