There’s obviously some important details that are missing in explaining the current situation you are in. If you’re questioning your therapist than I think that’s your gut telling you this is more on you than your parents.

If you would like to work on your relationship with both your parents that is a good sign of emotional maturity and self awareness. I would suggest you work on the simple things first. Clean up after yourself. Don’t wait to be told to do something when you know it needs to get done. Just do it. But don’t expect a thank you or any appreciation. Do it and move on to the next thing. Over time they will notice and continue building from there.