You are correct in saying that the Lord did not want the Israelites to intermingle with cultures that would expose them to harmful practices such as idolatry and child sacrifice. And, yes, women and children were included in some instances.

However, as we look at Scripture we always want to keep in mind the context of the passage we are reading. Each time the Lord commanded the Israelites to eliminate a particular people, He was definitely acting in accordance with all of His attributes, even ‘love’ and ‘mercy’.

In the case of the Amalekites in 1 Samuel 15:2 & 3: 
"Thus says the LORD of hosts, 'I will punish Amalek for what he did to Israel, how he set himself against him on the way while he was coming up from Egypt. Now go and strike Amalek and utterly destroy all that he has, and do not spare him; but put to death both man and woman, child and infant, ox and sheep, camel and donkey.’”

These people were descendents of Esau and enemies of Israel. They battled frequently with Israel and were a constant threat to them. God, being a perfectly righteous judge has the lawful right to carry out punishment upon anyone . This would not be considered murder, just as it would not be murder if we were to kill someone to defend ourselves or family or nation. We would be justified. There is a lawful time to kill, and this is the context of God’s judgment here. He is a just God and must punish sin. Because of their sin and rebellion against God, He used the Israelites to execute this judgment upon the Amalekites.

The same principles may be applied to the situation of the Amorites in Deuteronomy 2:33 & 34:  
"The LORD our God delivered him over to us, and we defeated him with his sons and all his people. So we captured all his cities at that time and utterly destroyed the men, women and children of every city. We left no survivor.”

God made it clear why these people were to be destroyed in Deuteronomy 9:5: 
"It is not for your righteousness or for the uprightness of your heart that you are going to possess their land, but it is because of the wickedness of these nations that the LORD your God is driving them out before you, in order to confirm the oath which the LORD swore to your fathers, to Abraham, Isaac and Jacob.”

The Lord is always faithful to forgive a nation, people, or person when they repent as He did with Nineveh. The Bible says He is slow to anger and abundant in lovingkindness. When Jonah went to preach to this nation, they were repentant. God had compassion on them and forgave them of their sins and did not destroy them then. However, 150 years later they went back to their sinful ways and it is recorded in the book of Nahum the prophecy of their total destruction which took place in 606 BC.