Therapy and Coming Out

So for starters, I learned about a program offered at my dads work that allows me 5 free therapy sessions every year. I want so desperately to take the chance, but I'm worried about what my parents will say to me. I think my mom would be a little more accepting than my dad, but he's a complete homophobe and transphobe and she has problems with judging people. I know I need the therapy, but I'm scared to tell them. What should I do? My sister has said that she'd be there for me and she'd take me out if anything bad happened, but I still don't know. Should I confide in my mom first? Should I find another reason to go to therapy other than for figuring out my gender?

As for coming out, I've told my best friend and she's willing to call me by different pronouns and a different name just so I can try it out. Again though, I'm scared to tell my parents, but I'm so sure of this. They have their suspicions, but not that I'm trans. I want to be able to cut my hair how I want and I want to be able to wear the clothes that I want. For right now I dress kind of androgynously but a little more on the feminine side because that's what I'm allowed. I'm only 14, but I've known for a while. Does anyone have tips for telling them?