Is it over stepping for a stepparent and non-custodial parent to limit how much spending money or pocket money a stepchild carries with them?

My 10 year old SD gets a sizeable allowance from BM with very little restrictions. When she's with us, I feel like there should be some sort of rules or limits to what she can spend.

On Friday I took SD with my kids to the store. SD mentioned needing some pen or styless thing for her computer drawing tablet, she'd left her's at school. It didn't seem like much but when we were checking out, it was like $35. I told her no, I wasn't spending $35 on some computer thing because she left hers at school, she could get it on Monday. I thought SD left to put it back on the shelf, but in the car, i saw she had it in her hand. I freaked and thought she stole it. She got super upset and said she'd gone to another register in the electronics department bought it, she had a receipt. When she pulled out the receipt I saw she had like $100 on her. She's 10. What 10 year old carries $100?

SD and I got into it in the car, she pretty much told me I don't have the right to tell her how she spends her money. I was livid, especially with my kids sitting there hearing SD say she doesn't have to do what I say. DH didn't back me up when we got home, since SD insisted she needed the pen thing for homework. DH told me she goes thru a ton of these things because she's always drawing on her tablet and the things break all the time.

Since then, I've been noticing that SD buys whatever the heck she wants. She doesn't ask us, she just buys whatever. It doesn't surprise me because I know BM is like this. I've talked to DH and he doesn't want to override what BM gives SD. DH isn't home during the day. SD's going to be here more next year when she goes to junior high. I just worry what happens when this kid gets older and she's spending money on whatever she wants.