Where did you get that he was "mouthing off" to anyone?
How is being mistaken as to whether his daughter was there or not make him guilty of anything?
Common police practice to ask you or not, you're not legally required to provide them ID, in most situations anyways.
1. "said he was sitting on a chair in a downtown skyway Jan. 31 when a security guard told him it was a private area and he couldn't be there. No signs were posted saying it was private, Lollie said. The guard called police."
- He is already upset at this point, because a security guard told him he couldn't be there.
"said police had responded to a report of Lollie trespassing in a private area and tried to talk to him, and he wouldn't cooperate"
- I assume he is still looking at his cell phone and not responding? Maybe "mouthing off" was the wrong terminology, but this guy is certainly not acting like he is "an innocent guy". I am always sure to at least act innocent when dealing with the police ala "no officer, I had no idea I was going that fast..." or "I had no idea this area was off limits, and that security guard sure is a dick".
2. It doesn't. It put him in the wrong place at the wrong time. If I knew my daughter was going to come walking by with her preschool class any minute, I would have just showed my ID and gone on my way. You can't decide to stand your ground and then point out that it was embarrasing for your daughter because her class witnessed this. It was his decisions that led to his daughter's class witnessing his embarrasment.
3. Legally required or not, and I am sure most law enforcement will agree, the person that refuses to show ID is the guily one 9 out of 10 times. We do not pay them to determine whether it was righteous indignation that caused him to not give his identifying information, it could just as well have been a warrant for his arrest that caused him to refuse. A police officers job is hard enough without the innocent folks giving them a hard time as well.