I actually worked on a case exactly like this some years ago. First of all, any decent lawyer who would take a case like this would do so on a contingency basis, meaning they don’t get paid unless you do and they take their percentage out of the settlement. You only pay for court costs and depositions (and the lawyer will usually let you pay that out of your part of the settlement, rather than upfront, too). That’s why accident attorneys only take cases that they think have merit.
At the time of the accident, you were a minor, but at the time of the settlement you are not, which is what matters. Your parents could certainly make a case that they should be able to recover from your portion of the settlement the amount of medical expenses they paid for you that were not covered by insurance and you should give that to them willingly because if you make them have to sue you for it, it will ruin your relationship and the attorney’s fees defending the case will eat up a large portion of the settlement. The court may rule that, since you were a minor, your parents would have to pay for your out-of-pocket medical care regardless of an accident, and that is part of the cost of having a child, but I wouldn’t begrudge them that reimbursement. Once you reimburse them for what they paid for your medical care after the insurance, the rest of the money is yours and will be for pain and suffering and any permanent impairment you may have suffered. Your mother cannot keep your settlement money. It’s yours. It will not be given to your parents in trust for you because you are not a minor anymore. It doesn’t matter if she paid the lawyer or not, it’s your settlement – it’s your money and the court is going to award it to YOU, not your Mom. The check will be made out to you, and you will be the one who has to sign the Settlement Agreement, not your Mom, so it’s not her call. I question your Mom’s judgment in hiring an attorney that didn’t take the case on a contingency basis to begin with. That was a mistake.
The big question you have to ask yourself is whether or not your relationship with your parents is worth X dollars. It’s your money, but is the relationship more valuable to you? Are your parents threatening to cut you off because they know that they can’t keep the money unless you let them (probably, if their attorney is worth a crap, because he or she should have told them that)? Is it emotional blackmail? The biggest question is whether you want to maintain a relationship with them and under what circumstances.