Was this reasonable cause for termination , or are these claims frivolous ?

LOL!                

You had a write-up, which was more serious than a  verbal warning. 

You responded to the writeup by acting even more immature. 

If you were fired for cause (sounds like your initial offense was serious) you haven't a leg to stand on. Evidently your performance at your coaching was such that you were removed from the building, as your dismissal was done in the end, by phone. 

I don't know if you need mental health help with anger management, or you've just been so kowtowed to you entire life you think you can do no wrong. Did you grow up getting trophies for participating?

Are the reasons frivolous? No.  Are they WEAK?  Yes. If you have some place to file a complaint, I would do so. A piece of paper is not a "weapon". That much is clear. But I have no idea what OTHER reasons they have for your termination. They could be mild, bad, very bad, or completely bogus--but you didn't give enough information in order to determine it. 

Speaking in a 'disrespectful' tone of voice may be tolerated by some, and not tolerated by others. Again, it depends on the severity and the actual things that were said. Threats or other indications that you were planning retaliation can be taken very seriously by almost everyone. Just be prepared for a high degree of scrutiny on your claims and theirs. 

Being disrepectful and behaving like you did is a legitamate reason to sack you as far as the employer tying what you did to their employee handbook terms, that is acceptable  so you have zero claim against the employer and likely unemployment will deny your claim as they may say you deliberately made yourself unemployed by your behaviour

In most locations, everything you describe is grounds for termination.

You can't have a tantrum and keep a job.

You are ineligible for unemployment.

It doesn't matter if you threw a piece of paper or you used a weapon.

Both are termination for cause. 

Shocking that you can't throw a toddler tantrum and keep your job, isn't it?

People who are reasonable adults don't throw things when speaking to management.  You clearly were not behaving as someone under full control of yourself.  

Businesses don't tolerate threats,  violence or anything else that indicates you are not controlling your emotions.  Not in this day and age.   They don't ban people lightly. 

Throwing a sheet of paper on the floor is obviously not an act of violence so take it up with somebody if it actually affects your future otherwise the people at the company or just going to get away with

Sounds like a first class ticket to termination. First you did whatever the first thing was then you were rude to a superior.