First of all stop lying to them about your intentions and reasons. The only way this will ever change is if they know the truth, go through the pain of accepting it and then and only then can you move on to your new level in your relationship. As long as you make excuses and lie to them about your reasons for not being home, nothing will change. It's the only way.

I'm not being insensitive here, I understand the reasons you went about it the way you did but I'm just saying it doesn't address the real problem. If they dont' know you're trying to be independent of them more and make your own life, how can they come to terms with it?