If your insurance has agreed to a settlement but you feel the dollar amount is not enough can you refuse the settlement?

You may want to try and sue the party first, if you except what the insurance company offers you then that is an admission of satisfaction on your part.

NO! Once you accept payment from YOUR insurance company (technically, once you cash the check), you surrender any right to persue the matter against the responsible party any further. Your acceptance of the insurnce company's pay out legally assigns your right to recover further back to the insurance company. If the settlement is large enough, many insurance companies will go after the responsible party to recover what they paid out to you (in insurance lingo, this is called "subrogation"). Make sure you are happy with what the insurance company is offering before finalizing things.