Actually he probably is past his date of appeal. I hope he is. If so, there's really not much he can do. If he were to appeal your claim, they would notify you. No way you can make it happen, or change what is happening at this point.
There would be an actual hearing, this time, in person or by telephone. But since your employer has already picked his reason why he was terminating you, and told that to the unemployment system before the first decision was made, it is not so easy for him to say, "oh no, wait a minute, I've changed my mind. She wasn't terminated for that reason, she was terminated because......." and cooking up some other totally different reason. So really, I wouldn't worry excessively about what has happened, what might happen, etc. The die is cast.
If he terminated you for attendance issues, he can now complain at a hearing about days you were supposed to work that he claims you didn't work. If he didn't terminate you for that specific issue, he can't now come in with all sorts of attendance records and claim you did something bad and here's the proof. But justified attendance terminations require that he had discussed your attendance issues with you, that you were aware that you were in danger of being terminated for attendance issues and chose to still not work the appropriate hours. It doesn't sound like this happened.
From the sound of the communication you're receiving, it sounds like he's just thinking up reasons between you and him, not connected with an unemployment claim in any way, that he doesn't think he should have to pay you that vacation time.
HOWEVER, there is BIG WARNING I need to give you here, concerning unemployment insurance. What you are saying, when you so carefully justify yourself as to how you and he both agreed on the hours you were available to work could sure get you in a heap of trouble if it comes up as an issue and ever gets discussed by the unemployment system!
Quote: "I also explained to him when he hired me that I needed a position that was remote and flexible because I'm a caregiver for my two children who are special needs. We discussed that before he hired me. Suddenly he's marking on a timesheet report about how I wasn't at the office for 3 hours each week even though he knew that I only had 5 hours available between dropping the last child off and picking up on those days."
No employer HAS to give you this sort of personal accommodation! This was, actually, very nice of him, and rather amazing to me that he agreed to it. There is NO labor law that would allow you to put this sort of restriction on your next employment and be considered able, available and actively seeking work. If you were to go into a hearing, or for any reason, tell the unemployment system about how he made this agreement with you, and you explained how you could only work......and so on and so forth, they will ask some very sharp questions about your availability for jobs and you may very well be disqualified for unemployment.
If I were you, I'd forget about getting the vacation pay from him. He's obviously going to argue about this until the cows come home. There is no law that demands he pay it. While he can't keep coming at you about it through your unemployment insurance, he will keep you jacked up forever.
It will never, once the decision has been made regarding unemployment insurance and the time for an appeal has passed, be an issue with the agency.
But if I were you, I'd never ever (to the unemployment system) mention that this employer ever gave you such an accommodation as he did. and never ever mention to the system that you need that sort of accommodation made for you in order to accept another job. There is no employer that is required to allow you to be off or to accommodate your childrens' schedules, special needs or otherwise. There's simply no labor law that allows for it or demands it. And you would lose your unemployment NOT because your employer appealed it, but because you removed yourself from eligibility by setting restrictions on the hours and times you would be willing to work. As you are receiving benefits, do not apply for any job that does not meet your needs. Do not go in to the unemployment system demanding all these accommodations or you will find yourself disqualified and possibly overpaid, not because of your employer, but because of what you yourself have told the agency.