I am very sorry to hear of your loss.
Well they did offer you a job. If there is some reason you thought they were required to accept your counter offer of part time work, you may have an argument.
It appears you have gone past the deadline to appeal the decision on your first attempt. You could call them and ask them how uch you have to earn to clear the disqualification. Or start a new claim asking for an alternate base year. - the previous dissqualification.will still be an issue, but they can tell you how to clear it.