The Law of the Lord is perfect...
Psalm 19:7
Q: Do you believe this passage?
A: I believe the whole Bible is true, and that would include Psalm 19:7.
Q: So then, would you stone your children according to Deuteronomy 21:18-21 for coming home 5 minutes late from their curfew?
A: Believing the whole Bible will occasionally bring up questions like this, and if you reject, reinterpret, or say that the capital punishment passages are not relevant, than what you're saying is that God's law is not perfect or that God has changed. In this case, the one raising this question is more intellectually honest.
With that in mind, let's revisit the question of "should we stone our children?"
If a man has a stubborn and rebellious son who will not obey the voice of his father or the voice of his mother, and though they discipline him, will not listen to them, then his father and his mother shall take hold of him and bring him out to the elders of his city at the gate of the place where he lives, and they shall say to the elders of his city, 'This our son is stubborn and rebellious; he will not obey our voice; he is a glutton and a drunkard.' Then all the men of the city shall stone him to death with stones. So you shall purge the evil from your midst, and all Israel shall hear, and fear.
Deuteronomy 21:18-21
This passage is clearly talking about severe and repeated disobedience, and also the despising of God's Word. This goes well beyond just coming home 5 minutes late, or stealing a cookie from the cookie jar. Capital punishment was taken very seriously.
Q: Well, what about for more serious things then, would you still stone your children?
A: I highlighted a very important part of the passage above. The parents are the ones initiating this process, but they're not the ones doing the stoning. The parents bring them to the elders of the city, who were in charge of the court system. Let's look at some qualities/characteristics of this court system.
You shall appoint judges and officers in all your towns that the Lord your God is giving you, according to your tribes, and they shall judge the people with righteous judgment.
Deuteronomy 16:18
Emphasis on the righteous part. That means not killing innocent people, or implementing capital punishment when it shouldn't be. Capital punishment was rare to be executed, and any judge in this system implementing more than 2 stonings within 7 years was considered to be bloodthirsty, and would thereby not be judging with righteous judgment like Deuteronomy 16:18 says.
And I charged your judges at that time, 'Hear the cases between your brothers, and judge righteously between a man and his brother or the alien who is with him. You shall not be partial in judgment. You shall hear the small and the great alike. You shall not be intimidated by anyone, for the judgment is God's. And the case that is too hard for you, you shall bring to me, and I will hear it.'
Deuteronomy 1:16-17
Keep far from a false charge, and do not kill the innocent and righteous, for I will not acquit the wicked.
Exodus 23:7
Clearly the Bible and God does not support capital punishment on someone who is innocent, or for offenses that are not worthy of capital punishment (like the example of someone who comes home 5 minutes late of their curfew). There was an extensive investigation, with all parties being given a fair evaluation.
then you shall inquire and make search and ask diligently. And behold, if it be true and certain that such an abomination has been done among you,...
Deuteronomy 13:14
You also need more than just one witness for this case.
A single witness shall not suffice against a person for any crime or for any wrong in connection with any offense that he has committed. Only on the evidence of two witnesses or of three witnesses shall a charge be established.
Deuteronomy 19:15
So to answer the question at hand, no, I would not stone my children, for several reasons, none of which involve "picking and choosing" what parts of the Bible to accept/reject. First, it's not even the parents that do the stoning, it has to go through the elders and the court system first. Me practicing the capital punishment laws in Deuteronomy 21:18-21 (and other places in the Bible) would actually be breaking the Biblical laws. These laws were given for the Biblical court and the elders, just like there are laws for men, laws for women, and laws for children. And in this regard, the question of "do you stone your children" is invalidated since this isn't a law for the parents to execute, but for the elders and the courts.