You cannot get a legally valid power of attorney without your mother's consent. You want her to agree to and sign what's called a "durable power of attorney for finances."[DPA]
It's called "durable" because the person appointed agent (you) can continue to represent and act for the principal (your mother) even if she is incompetent. However, your mother's signature on a financial DPA must be notarized. If your mother is unable to get to a notary public (or you couldn't bring one to her) the DPA would not work.
DPAs for finances are definitely NOT for "crazy people." Many healthy, competent people have prepared financial DPAs. Then if, for whatever reason,a person becomes no longer competent to manage his or her own financial affairs, the DPA provides an easy, legal way for the agent to do that managing.
If your mother refuses to agree to a financial DPA, your only option is to file a court proceeding, seeking to have her declared legally incompetent and you appointed as her custodian. Court proceedings here are bound to be unpleasant. Perhaps if your mother realizes that a court proceeding might be filed, she'd become amenable to signing a financial DPA.