Both are good. For the first one, you could also say: It's not that I'm apologising so that you'll forgive me I'm not just apologising so that you'll forgive me The phrase 'in order for' is more formal, and would be less common in conversation. Incidentally - 'apologising' is the British English spelling.
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sarabaIt's not that I am apologizing in order for you to forgive me.The first of the two makes your message clearer, but both are acceptable.
The reason why I am apologizing is not because I want you to forgive me.