A couple of things to note. First I'm going to define the good-evil law neutral spectrum then I'll address the notion of how binding they are and finally I'll touch on your specific situation.
So the good-evil spectrum is principally defined by how bound you feel to your community/the greater good vs how much you value your own success. A good character will tend to want the best for the kingdom, village, etc even if it means some sacrifice to them self. A neutral character will attempt to do what's best for others, though will be less willing to have personal sacrifice. An evil character is always looking for personal advancement, although sometimes that may align with other's interests.
Law-chaos is defined by an adherence to the laws of the land. Lawful people abide exclusively by what is legal. Neutral characters respect the law but may see circumstances where breaking it may be necessary. A chaotic character respects the law only so far as the direct consequences, ignoring it whenever they feel necessary. Chaotic characters may sometimes also have a tendency towards vices and unpredictability, though this is more flavor than an actual denotation. Also you should note that a lawful character may not abide by the law of the land but instead by the tenants of a cult or their own moral code. A player needs to define this and be consistent with this.
Actions define alignment. With newer players I'll tell them when their actions conflict with their alignment, though I try to make clear that a single evil/chaotic act does not change their alignment. A lawful good character may desire to depose an evil ruler even though that is a chaotic act, this is entirely permissible. If you see someone regularly disregarding their alignment ask them if they'd like to change it and that's fine. If repentance is necessary, take care of that in game through denying spells or a cleric talking to the character. Alignment should be a guide for roleplay and only has limited mechanical involvement.
I don't think any group can function with polar opposed alignments (CE and LG in your case). Simply without regular large stretches in roleplay the characters will find their motives and goals do not line up in any way and so their isn't a reason for them to be together. The further apart the characters are in motives and methods the more tension their is and I'd recommend CONSIDERING having a character bow out of the group because they should really hate the group, perhaps (with player permission) turn them into an NPC. This will not work with every group, it's just something to consider.