I can't really help you on how to convince your parents since when I started cosplaying I was an adult and my parents actually love what I do. I can help you on the jacket though, since I've made it before
. I used this pattern
, just extending the front opening on the left side to be wider like hers. I made it out of polyester gabardine and lined it in regular old lining fabric. The edging is red double fold bias tape and the thin red detail is some cording I found and hand stitched down. The zipper is just a little one I found in the store and added the red bias tape around it and stitched it down. The patch I had made for us and ironed it down. The beads my friend who cosplay Lenalee made for both of us. Unlike some Lenalee cosplay, my friend's skirt is made into her jacket because when she removes her jacket in the manga, it looked like the skirt was attached. We just made that out of a sturdy cotton. We also made her shorts, gloves, and shirt
to go under it. The shirt and gloves are made out of a two way stretch fabric and the shirt has a zipper up the back. The shorts are made of the same polyester gabardine that her jacket is made of.
If you want any more detailed help, let me know and I will see what I can do.