ANSWER: While the Bible does not precisely state all of God's reasons and motives for doing something, we can take what information is available and derive possible explanations. Although it may seem outwardly there was nothing wrong, to God nothing is hidden! The issue surrounds the circumcision of a son. I will speculate as to why it was not done at the proper time, on the eighth day after birth, as God commanded.
The Bible states that while Moses was in Midian he was told to go back to Egypt (Exodus 4:19). He soon travels to Egypt with his wife and sons. Exodus states that during the journey 'the Lord met Moses and tried to kill him.' It is then that Zipporah, his wife, did something seemingly odd.
24. And it came to pass by the way, in the inn, that the LORD met him and sought to kill him. 25. And Zipporah took a sharp stone, and cut off the foreskin of her son, and threw it at his feet, and said, "Surely a bloody husband you are to me." (Exodus 4:24 - 25, HBFV)
Zipporah's rather assertive act saved her husband from certain death (verse 26).
Because only one of his sons is mentioned here - not having been circumcised, we must assume the other was! Evidence suggests that Moses did circumcise his firstborn according to the command of God. Was Zipporah (not being an Israelite) so appalled at the bloody act that she gave her husband a hard time over it - such that he didn't want to do it again? God knew about the situation and gave him time to repent. Moses may have hoped the problem would be forgotten and go away.
Circumcision on the eighth day after birth was part of the covenant between Abraham and God (Genesis 17:10 - 14). This act became part of the agreement between God and Israel. Every male child had to be circumcised or else 'that person shall be cut off from his people' (Genesis 17:14).
Not only was Moses head of his household, but God had picked him to be head of the whole nation of Israel - he was now going to make a decision - circumcise the boy - or die! Him and his wife must have discussed the matter and she knew he was dying before her eyes, making her quick to circumcise the boy! But she was still upset over having to circumcise her son. There is more that is not recorded that took place, but is alluded to in Exodus 18.
"Then Jethro . . . after he had sent her back, with her two sons, of whom the name of one was Gershom . . . the other was Eliezer" (Exodus 18:2 - 4)
Why had Moses sent his wife and his sons back? More speculation here - because his son was most likely a young boy, not a baby or small child, circumcision would have made him unable to travel without great pain. And because he did not have much to say on this matter here in the scriptures, he would have been embarrassed to have to explain the circumcision to a young boy - that is also his son. This would have put him in a bad light before all the people of Israel. I think it was likely the ordeal with his wife over the circumcision that caused him to send his family back to his father-in-law's house.
Before of the painful of circumcision, Zipporah needed to stay at the Inn with the boy until he was able to travel - influencing Moses' decision to send his family back to Jethro's house. Discerning the scriptures and how Zipporah was a woman who spoke her mind - and most likely not have let up on her husband all the while they were in Egypt - if he hadn't sent her back.
Zipporah took the foreskin of the circumcised boy and threw it at the feet of Moses along with mouthing her disgust with doing it! God no more mentions Zipporah after Exodus 18 and her sons are not mentioned with any degree of importance anywhere else in the scriptures.