You are supposed to be accepting all the available work that your boss has for you when you are out of work due to a situation like this and you were not fired from the job.
If you are drawing benefits due to the employer not having enough work for you, and you refuse to come in and work just the part-time hours they may have, you are committing unemployment fraud,and you will end up having to pay back each week of unemployment where your employer actually offered you a shift and you refused it.
All they have to do is report you to the unemployment system as having refused a shift, and you will be sunk. Each time you certify for a week, you answer the question about did you work, refuse work, quit a job, etc. That question must be answered honestly. The employer will have documentation about how much you worked, when you worked and if you were called and refused the work. The unemployment system will see this information. It needs to be in perfect harmony with what you have told the unemployment system while filing for benefits.
However, if you are taking those shifts and working with your unemployment to cover weeks when you did not gross at least $275, or whatever your weekly basic allowance is (amount you are entitled to with unemployment) you can use both work and unemployment to supplement that work.
For weeks you work and actually make less than your WBA, you may be able to draw partial unemployment. For weeks you do make more than your WBA, and then do not work the following week, you will reopen your claim and file again for a week of unemployment. That's how it is supposed to work.
If you filed for unemployment, and your reason is that you quit because your employer didn't have full time work available for you, you will not be approved to draw benefits. If you are fired for refusing shifts, regardless of whether or not they are full time, you will not be approved to draw benefits, because you're not out of work through no fault of your own, you're out of work because you don't want to work less hours, even when offered those hours and working those lesser hours are in the best interests of the business. It sounds like they are giving you all they can.
Take some unemployment, if you qualify, and continue to work all the hours they have available for you until you find something else that is full time or until your employer gets back on their feet again. But do not file for a week of unemployment if approved when you have turned down work that you were offered without reporting that you were offered this work and refused it. Believe me, they'll find out, and you'll be caught up for doing this. You do not want to be found committing U.I. fraud in FL right now, I promise.
