Also, just to be positive, be sure you are making the required weekly certifications for benefits. If you were to be approved, you'd be back paid only for weeks that you had certified for since you filed the claim.
Be well organized in your responses to the adjudicator's questions. Keep in mind that in spite of what you signed, you did NOT quit the job due to family reasons. You quit the job because of the terrible awful working conditions, after making management aware of the working conditions and situations that you were having trouble with, and making every reasonable effort to solve the problems without quitting the job. You decided that you had no reasonable alternative to quitting, because the job was causing you extreme emotional distress in spite of your good faith efforts to do a good job and to work out the situations with the employer. You could even say that you felt there was a concentrated effort to force you out by treating you significantly badly once you had begun to speak to people and try to get the situation changed.
But remember, the unemployment system is not the EEOC. It is not their job to provide you with unemployment just because you were exposed to racist comments or some sort of illegal mistreatment due to sex, race, creed, religion, etc. There's no automatic thing that if someone said something racist to you, that bears more weight than if they said they didn't like your green socks today. Don't make too big a deal of anything except that you spoke with your managers and with HR, and attempted to resolve the situation.
It is my suspicion that you will probably be denied in the initial appeal. If this happens, you will receive a notification that you have been denied, probably because you voluntarily quit your last job for personal reasons. You continue to make weekly certifications. You file an appeal, in which you do not have to make your argument, you merely state that you disagree with this decision denying you unemployment benefits and you wish to appeal it.
You will be given a time and place for a second hearing, at which the employer may also be present. At this time, another hearing officer will listen to both sides of the case and make a new decision about whether to grant unemployment. You never again mention that you signed something saying you quit for family reasons. You will, in this hearing, if you are asked about why you signed this, simply explain that you were told or encouraged to say this, rather than referencing the terrible work situation, so that you would be able to get a good reference from them.