I think you have drawn a line in the sand needlessly. And she is doing what teens do... testing that line. Mandie is a perfect way to push you. She's succeeding! :)
As for the makeup, yes, a ton of 13 yr olds do wear it. Most wear too much and don't apply it in an appropriate manner for a mature young woman. Most wear it like a 13 yr old who is trying to look mature. ;)
My daughter is 12, in 7th grade. I took her last year to the cosmetics counter (Clinique) and let them apply what would look nice with her skin and coloring. I told them I didn't want her to look "made up", but, like I had told my daughter, to bring out her own natural beauty. I don't wear my own makeup like "war paint" and never have. And for years and years I have made my preferences about such things known in subtle ways. We have a niece in our family who is very "artsy" and does hair for a living (she's older). She has several (very large) tattoos, and wears extremely bold makeup. It's not my daughter's style. And we have discussed her cousin and "her" style.
My daughter wore some of the makeup we purchased for a few weeks, but mostly reverted back to lip balm only. It is just too much work and hassle for her most days I think, and she is confident in herself and doesn't "need" it. She is stunning when she wears it (to my 'Mom' eyes at least) and does indeed look older than her 12 years. But she still wears it tastefully even then.
Powder foundation, neutral/natural eye shades, soft lip color. She applies mascara better than I do. LOL---when she wears it... which is about as often as I do--maybe 3 times a year.
There are other older cousins in our family (late teens, not adults like the hairstylist) who wear full makeup everywhere. But they also wear a more toned down style that looks mostly natural, except there is no mistaking the lashes,LOL.
Lead by example, and take her to a place you trust to TEACH her how to wear it. Then buy her what you are comfortable with (color scheme wise) and let her play around. She's not too young.