My bank doesn't issue cards to anyone under the age of 18, but in terms of customer service my bank is 1000% better than any of the ilk of Wells Fargo/BofA/etc., so I'm not going to change my bank just because the ice cream shop requires a bank card.
Rather, she can use a FamZoo or Greenlight card if we feel like paying a monthly fee for the privilege of being able to buy ice cream from that one shop. But I'm starting to think it's not worth it, since there's a Trader Joe's around the corner that sells a better product and accepts cash.
Sorry your bank is so feature poor but glad you like it. USAA is an awesome bank so would love to learn more about a bank that’s 10x better. Also, my local credit unions offer this common feature.
But it seems like you’re blaming your the ice cream store for your own and your bank’s shortcomings.
You can also just get a second credit card and give it to your kid and have your kid make purchases in your name since the ice cream shop isn’t likely to care.
You could also load a card onto her phone and have her pay with that.
Every 11 year old in my neighborhood in the US solved this problem, so I wish you the best of luck with your struggle.