The backstory of the visit of the three men and promise of Isaac includes chapters 15, 16, and 17 of Genesis.  And there is a lot of trouble between the promise of Chapter 18 and the fulfillment of Chapter 21.  

Genesis Chapter 15: The promise of a child is made long before the visit of the Lord at the Oaks of Mamre. It could be that Sarah’s laugh is less about her physical condition and the status of her relationship with Abraham than it is how absurd it seems for God to make such a promise after having failed to make good on the original promise of chapter 15. 

Notice that the promise made in Chapter 15 is given to Abram and Sarai. They have not received new names yet. To receive a new name is to transition to a new state of being, which happens often in the Old Testament (as with Jacob becoming Israel) and in the New Testament (as with Simon becoming Peter, and Saul becoming Paul).  

Genesis Chapter 16: Sarai has given up on having a child, given up on trusting the promise of God, and in fact blames God for failing her:  ‘You see that the Lord has prevented me from bearing children (Gen. 16:2b).  She then takes matters into her own hands by “giving” her Egyptian slave, Hagar, to Abram, so they will not remain childless. Jealousy and envy lead Sarai to abuse Hagar when she becomes pregnant. She goes to her husband to complain, but Abram makes no effort to involve himself in any way, simply telling Sarai to do whatever she wants to Hagar; thus Hagar runs away to escape Sara’s abuse.  

What then happens is a story we do not often tell.  

An angel visits Hagar and promises to make a multitude of people from her offspring, the same promise given to Abram and Sarai. 

Genesis Chapter 17: The covenant with Abram and Sarai so far has been of words only. In Chapter 17, God gives Abram and Sarai their new names–Abraham and Sarah–and gives them a sign to mark the covenant with them, and oh what a sign–circumcision!

All of the males, Abraham himself and all of the males in his household, including his 13 year old son, Ishmael, suffer circumcision.  We pass over this covenant without much curiosity, but what is it about circumcision that makes sense as a sign of God’s covenant with Abraham?  Is it somehow related to the nature of the covenant itself, having to do with procreation? 

And women are left out altogether. 

What kind of power and authority does Abraham have to be able to insist that all males be circumcised? 

In any case, circumcision as a sign surely dispels the idea that covenant with God is easy, requiring no change, no sacrifice.