Actually if you want a good secured card, go to US Bank. If you are already there, we should be good. My cousin said they don't report secured either.
Ok to OP:
Remove yourself from your parents' account. Wells fargo is very conservative. That late payment from Chase on top of your previous deliquent account with them probably scared them off. You can dispute it with the credit bureaus directly, by going to their website, and file a dispute with each of them.
Secondly, to clear misconception.
You CAN max out the card. As long as you pay in full, that does NOT affect utilization. Utilization is calculated by taking whatever you spend MINUS whatever amount you paid. So if you had a 1000 dollar CL card, and you spent 1000 bucks, then you paid 900 bucks and owe the remaining $100. Your utilization in this scenario is 10%. If you had paid in full, your utilization is 0%.