Regardless of what happened in your unemployment hearing, this is a closed system. in other words, no other employer is going to find out that you were accused of theft by your former employer through anything that comes from the unemployment insurance system. No one but you or the separating employer (or your legal representative) could ever obtain any information about the claim.
Since their original story was that they were letting you go due to a change of direction on the company, you were not discharged for one false allegation. You were not even denied unemployment benefits for that false allegation. Them making a false allegation during the claims process is NOT something that is going to ruin the rest of your life, and you are not able to sue them for saying that during the unemployment process. There is, in this sytem, the assumption that one or both of the parties may be lying. They go with the "most believable." Obviously, that was you and you are currently receiving unemployment insurance, which indicates to anyone who knows anything about it that you were not let go for a misconduct reason. I'd say the chances that they're currently trashing your re-employment chances and telling people who request a reference that you were discharged for stealing is VERY slim.
That you have not found another job is not something you can dump totally at the feet of a former employer. It is a reality that hits millions of people a week. You were in a very high income situation. You were in the same industry, and even the same position for a long period of time. You're expensive, and frankly, you may have been becoming dated, as far as your skill set is concerned. At least, the employer could possibly have cut their operating cost by hiring a younger, less experienced person at a very much lower salary, and that's totally legal for them to do in an "at will" state, which yours is.
I would suggest that you contact a veteran's employment specialist at your local Career Center, possibly seek some counseling through the VA for your depression issues. These are practically inevitable in a job loss situation such as you are experiencing. But there's nobody you can sue for doing it to you. You are obviously taking this issue all over your family life, where you and your wife are not supportive of each other. This you perhaps cannot help, but you CAN help your daughter see how her dad deals with adversity. Set her a good and courageous example.
Instead of looking for others to blame and sue, you can work on moving forward with this. Call prospective employers, not attorneys. No, you do not have a case. You cannot sue an employer for letting you go, regardless of how much hardship it has caused you. The one venue where you could appeal and change what happened, which was unemployment, you prevailed. You won. Now, move forward. Perhaps update your skills. Downsize if you have to. Try a new industry or a new type of work, you're not really old. You have many years to move on.