When I was a Christian, I think it's safe to assume that I was one of those children that you refer to. When I talk about my experiences with God you can assume that I'm referring to those experiences I believed I had as a Christian.
I'm sure you've heard this before, but Christianity isn't something you just try out for a little while to see if it works. You're either saved or you're not, and once you are saved, you can't lose it. So either you are saved, and right now you are severely backslidden, or you were never saved in the first place.
For purposes of argument, I'm fine expecting God to act like a parent only to Christians. But if you believe that God gives special treatment in this world to those who cleave to his chruch then you're in for considerable disappointment.
I never said I believe Christians get special treatment from God in this world. I believe quite to the contrary, actually. II Timothy 3 says that all who live a godly life in this world will suffer persecution.
Why doesn't God look out for Christians, at least?
God has looked out for Christians. He's given us salvation and eternal life. The Christian realizes that this world is not our home, so trials and hardships are just a temporary thing, and very insignificant when compared to the ultimate destination of being with Christ forever in heaven.
I would expect good things to happen to Christians and bad things to happen to everybody else, not bad things happening to everybody.
Again, this is not the case. Christians suffer in this world because this world is under the curse of sin and because the ruler of this world is Satan. Satan wants to make life as hard as possible for Christians, so he attacks them. And I'm sure you're asking right now "Well, why doesn't God stop him? What kind of all-powerful God can't even stop Satan from attacking his children?" I'm sure you're familiar with the story of Job, right? When God said Job was a righteous man and served Him, Satan responded by saying that he only did it because God had blessed and protected him. So God took away the protection, and allowed Satan to persecute Job. In the end, when Job was at the lowest point in life, he still glorified God. And this is one of the reasons why God allows persecution to come to His children. He is glorified when His children praise Him in the midst of troubles.
Let me guess.... you're saying "What kind of sadistic, selfish being allows others to be persecuted so that he can stroke his ego?" Right? Is that what you're thinking? Well, this is not a simple thing to understand because we are human, and for us to do it, it would be pride. But God is God, and He is worthy of all glory and praise, so for Him to do it, it is just.