legit nursing bra issue... help!

bought nursing bras today. platex. the “over the boob” piece unhooks and comes down - i get that - to expose the nipple for nursing. but then in the bottom layer of the bra is like a piece of fabric that doesn’t even go over the nipple, it like goes on your side of your boob??!

so

1- what’s the point of that extra inside piece of fabric?

and

2- the bra is so thin my nipples pop right out of it and thus would show through any dress or shirt i have on! i can’t do that!!

anyone have a solution or better bra that doesn’t do that?! i’m so frustrated.