The following is an excerpt from Dr. Thomas Holland's Crowned With Glory, ©2000, used with permission.
Luke 2:22 - "of her purification"
And when the days of her purification according to the law of Moses were accomplished, they brought him to Jerusalem, to present him to the Lord;
Here the variant is small but the difference is profound. The Authorized Version and Textus Receptus (Beza's edition and Elzevir's edition) use the phrase, "of her purification" (katharismou autes). Modern versions and the Critical Text read, "of their purification" (katharismou auton). Contextually, the reading must stand as reflected in the KJV. Under the Levitical Law a woman was considered unclean after giving birth and needed purification. The passage in Leviticus 12: 2-4 reads,
Speak unto the children of Israel, saying, If a woman have conceived seed, and born a man child: then she shall be unclean seven days; according to the days of the separation for her infirmity shall she be unclean. And in the eighth day the flesh of his foreskin shall be circumcised. And she shall then continue in the blood of her purifying three and thirty days; she shall touch no hallowed thing, nor come into the sanctuary, until the days of her purifying be fulfilled.
The citation is quite clear: this was "her purifying" and not the purifying of both mother and child. Therefore, the Authorized Version and the Greek Textus Receptus agree with the Levitical Law.
To offset this point, some have suggested that the word them is a reference to Mary and Joseph. The argument is that since Joseph and Mary are mentioned in verse 16 and referred to in the second half of verse 22, the word them referred to the married couple. The obvious doctrinal problem with this is that under the Law of Moses, as set forth in Leviticus 12, the woman and not the husband needed purification after giving birth. The best contextual reading agrees with the Authorized Version, as it would support both the Old Testament Law and the actions presented in Luke's Gospel. 
Admittedly, the Greek support now known for the reading as found in the Textus Receptus is extremely poor. It is found in a few Greek minuscules such as 76 and a few others.  There is an additional textual variant within the Greek manuscripts. Codex D05 (sixth century), which is highly acclaimed among textual scholars, has the reading autou (of it). While the reading autns (of her) is preferred, both readings stand in the genitive singular and not the plural as auton (of them). Additionally, we find the Sinaitic Syriac and the Sahidic Coptic versions supporting 2174, and D.
The reading her purification has a great deal of textual support among the Latin witnesses. The majority of all Latin manuscripts read, et postquam postquam impleti sunt dies purgationis eius secundum legem mosi (And after the days of her purification, according to the law of Moses). The Latin word eius (or ejus) means her and stands in the feminine genitive singular, thus of her. In order to have the translation of them, the Latin texts would have to use the word eorum. When we consider the age and the number of extant Latin manuscripts, we find the reading is both ancient and well substantiated. It is also interesting to note that the reading has some support in the forged Gospel of Pseudo-Matthew (possible third century). Written in Latin, it allows us to see that the purification spoken of in Luke 2:22 was a reference to Mary. Pseudo-Matthew reads: "Now, after the days of the purification of Mary were fulfilled according to the law of Moses, then Joseph took the infant to the temple of the Lord" (15:1).
 There is a debate among textual critics regarding eclecticism. Most support what is commonly called "reasoned eclecticism" which tends to focus on the age and number of existing Greek manuscripts. However, scholars such as G. D. Kilpatrick and J. K. Elliot promote "rigorous eclecticism" which focuses on the internal evidence above the external textual evidence. Therefore, according to this type of eclecticism, any textual variant regardless of age or number could conceivably be the correct reading if the internal evidence is sufficient. See Kilpatrick, 33-52.
 Edward F. Hills, The King James Version Defended (1956; reprint, Des Moines: The Christian Research Press, 1984),, 221.