Important decision to make?!?

So I got offered this internship that I really really wanted. I’m ecstatic right now because I was competing against other girls. It was this lady who is the owner of a small buisness and the internship is perfect for me. The only thing is that I got another job as well and they both start on the same day. I would like to be able to do both but if I had to choose I would choose the internship. I talked to my dad on the phone and he said to let the internship lady know but I’m so non confrontational and don’t want to seem unreliable. How do I let her know my other job starts the same day and that I want to still pursue the internship?