I'm not sure what you're asking. Our Lord was asked the following question (by a lawyer no less):
Christians do love God and they show this love by enacting justice throughout the world. They illustrate their love for God through numereous charible works. But it is all because of God working through us. I suspect that you would agree that you cannot name one good act that you've done on your own for someone without the help of God.
Did anyone, anywhere ever suggest that we succeed perfectly? It's the goal toward which we strive. Unless, of course, you deny that we can or should strive. (I'm reminded of teachers who think that any test on which anyone in the class gets 100% is not a real test!)
Man cannot live by the laws and commandments no matter how good they are.
To the extent that someone is "good," isn't he living by the commandments?
Man relies upon God's grace and mercy for when we fail to keep the commands.
So we don't rely on God's grace and mercy when we succeed in keeping a commandment? Oh, wait . . . unless we never keep them. Does God issue commandments, the fulfillment of which is necessary to eternal life knowing that we cannot keep them, even with His grace -- so He decides arbitrarily that some will be exempt and saved anyway?
Christians do love God and they show this love by enacting justice throughout the world.
The "justice" that chooses some and rejects others arbitrarily? Not quite sure what you mean here, but there seems to be little enough justice here below.
They illustrate their love for God through numerous charitable works.
Maybe it's not what you intend, but the way you say this seems to make clear why "as cold as charity" is an old expression! Since you're not specific, I can only assume you mean by "charitable works" such common forms as almsgiving in whatever form and perhaps volunteering. We are, of course, commanded to give to the poor, but that's a separate commandment from that of love of neighbor. Almsgiving without love gives us the horror of the welfare state. Are you suggesting that the rich don't count as our neighbors or that the destitute are somehow exempt from the commandment to love our neighbor?
So what does "love of neighbor" mean? To me, it's to keep the awareness that each is made in the image and likeness of God, however sadly or horribly that image is obscured in a given individual; to remember always that, as God is love (a point on which you agreed), He loves each immeasurably and more than we can imagine; He can do no other than love -- to say which is not to put a limitation on His power than to say His power is limited because He cannot create a square circle. God doesn't do nonsense.
But it is all because of God working through us. I suspect that you would agree that you cannot name one good act that you've done on your own for someone without the help of God.
Can't argue there -- but God not only created us, it is His love and grace that keep us in being at all! Should God -- per impossibile -- cease to love us, we simply would cease to be at all.