Thank you for your question today, I look forward to assisting you. I bring nearly 20 years of legal experience in various disciplines.
Ok. I'm not sure what other attorneys you have spoken to, but they did know enough about employment law to get one thing right here. "At will" employment is a type of employment that most of us in this country are under.
It legally means that the employer can terminate your employment at any time, with or without cause. They don't have to give warnings. The reason for the termination doesn't have to be of a particular level of seriousness. The termination can literally be for nothing. Here though, it was not without basis. You stated that you were 45 minutes late to work.
Despite your belief that this is "definitely not grounds to fire me" it actually is completely legitimate and legal grounds for termination. It is more than sufficient to justify termination, not because it is some terrible thing. I've been late before too. I'm not judging you in that at all. The point though is that, in an "at will" employment situation, they don't even need a reason. When you don't need a reason, something as insignificant as being 45 minutes late is absolutely legally sufficient to justify termination.
So, the termination is legal here. Where you can fight the issue is unemployment. While the employer's basis for termination doesn't have to be particularly significant, their basis for blocking unemployment does have to be significant. They have to show that you engaged in misconduct worthy of blocking your unemployment. So, in your appeal, you need to lay out that you have not had a problem with tardiness and that this is the first time you have been late to work . You accept that it was wrong to be late, but this is not something you have done regularly. You've not receive numerous warnings about it. Your history with the employer is good, except for this incident.
That is the argument that you have to make. Also, if anyone else there has been late, but was NOT terminated, you need to raise that issue as well. Then you can state that this is not a regularly enforced policy of the employer. That will also strengthen your unemployment claim.