The Catholic Church did not "delete the 2nd commandment" or "make an addition to the 10th."
For starters, the commandments are not enumerated in the original text. There is simply a list of do's and don'ts. How to break them up is a matter of opinion. In addition, the Bible has two accounts of the 10 commandments. One is in Deuteronomy 5:7-21 and the other is in Exodus 20:3-17. Each "version" is worded slightly differently which also adds to the difficulty in determining how the commandments are divided.
In Jewish tradition, the 10 commandments begin with a commandment that is found in neither the Catholic nor Protestant traditions. In Jewish tradition the first commandment is found in Exodus 20:2 "I am the LORD your God, who brought you out of the land of Egypt, out of the house of slavery." This commandment is considered separate from Exodus 20:3 "You shall not have other gods..." Their tradition has understood the first commandment to be a call to belief in God. Should they then accuse Catholics and Protestants of deleting it? Or is it simply that the different religious traditions have simply come to different conclusions about how to divide up the verses?
According to the Catechism of the Catholic Church
the 1st commandment is:
THE FIRST COMMANDMENT
I am the LORD your God, who brought you out of the land of Egypt, out of the house of bondage. You shall have no other gods before me. You shall not make for yourself a graven image, or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth; you shall not bow down to them or serve them. It is written: "You shall worship the Lord your God and him only shall you serve."
As you can see the sentence about not making graven images is indeed included in the Catholic understanding of the 1st commandment. It has not been deleted. The Catholic tradition simply has understood all of those verses to be a single commandment about right worship of the true God.
As for the 9th and 10th commandments, we face the same situation.
You shall not covet your neighbor’s house. You shall not covet your neighbor’s wife, his male or female slave, his ox or donkey, or anything that belongs to your neighbor.
- Exodus 20:17
You shall not covet your neighbor’s wife. You shall not desire your neighbor’s house or field, his male or female slave, his ox or donkey, or anything that belongs to your neighbor.
- Deut 5:21
Are they a single commandment or do they have enough difference to be considered separate? Does the grammatical structure signify a single idea or two or more?
Jews, Catholics and Protestants are all using the same verses of Scripture. None are deleting or adding anything. We are all just arranging them differently.