I think its a great idea Indie. why would your parents be worried about it? Let them know you will be doing EMDR and you feel you need more time with your therapist and that you are willing to pay for the extra time with her. If its not coming out of their pocket i dont see why they wouldnt agree. if the worry is for your mental health, assure them that the increased time is not an indicator that things have decompensated with you, just that you are at a point that you are wanting to work harder in therapy to move forward so yu feel increased time is needed and you are willing to pick up the tab to do so.