My daughter is 26 and made less than $4,000 last year and I provided most financial support for living expenses. Will she be able to file taxes if I claim her?

Any person always reports their income earned from working on a tax return in their own name, regardless of whether they might also be a dependent of someone else.  (The only time a parent might report a child's income on the parent's return is if the child is under age 18 and has certain investment income only.)

Your child can be your dependent if they have less than $4300 of taxable income and you provided more than half their support.  It is not a requirement that they lived with you.  When your child files their own return, they must check the box for "yes I can be claimed as a dependent by someone else."