First to the OP, it sounds like you did a very good job of dealing with a very unexpected phone call. Kuddos to you.

If you do a google search for "Mark Morsch", it shows he is a personal injury lawyer in Florida. If you search within the results for "Tigger", it comes up with 276 entries.
One of the first interviews that came up was CBS News This Morning from Monday, Jan 8, 2007. Mark Morsch is already identified as their attorney. The interview says the 'Tigger Attack' took place on "Saturday" - so less than 2 days after the incident, they were already on national news giving interviews.
Also, if you go to the
link for the police report, you can see that
the police officer who wrote out the report, spoke with Mr. Monacho on 1/5/07 at 2200 at 2200 hours (10:20 pm). The report indicated Mr. Monacho says the incident occurred at about 12:30 pm on that same day.
The report also indicated that the incident had already been reported to the General Manager and to the Entertainment Manager.
This report also says that the officer who wrote this report had spoken with Officer Finlay, who had responded to the incident and gotten a statement from the Tigger performer (basically, that the performer could not see his handler and had gotten choked and knocked off balance by the person behind him).
It shows that the dad saying the only way to get a police report filed was to go to the media is not true. Already by less than 40 hours after the incident, he had gotten enough press to get on a national news show.
Most of the TV reports only showed the actual 'hit', and many of them showed the video zoomed in to show only Tigger and Jerry Jr.
Watching those gives a very different view of what happened. i don't have a link to the raw video, but that's much better than watching the heavily edited bits shown on TV.
The raw video shows much more - watch Tigger's nose, which is what he sees out of. When he is posing with the mom and the little kids, he spreads his arms out (in sort of a typical Tigger pose). I think Jerry and Jerry Jr took the spread arms to be an 'invitation' to make more room so Jerry Jr could get into the photo. If you watch where Tigger's nose is pointed though, you can see that he doesn't know Jerry Jr was there until the arm comes up behind him. Then watch the feet - Tigger's are up against the curb. If he fell, he woudl have either fallen forward and hit the small kids - who he knew were there - or back over the fence - which he also knew was there.
There is also an early part of the video, where the dad puts the camera down (you can see the ground on the video) to get into the picture himself. You can only see the ground, so you can't see what happened, but you can hear. Sounds to me like the dad left Tigger suddenly and says "Sorry. My bad. I was messing with your head." (I can't remember the exact words - he either says "messing with" or "in").
The dad's explanation of that in the CBS news Report was that "I attempted to get in a shot with Tigger when he stuck his arm out and I figured the photographer could get a shot with two little guys," father Jerry Monaco told The Early Show co-anchor Hannah Storm. "At that point he started bumping into me and I apologized and I figured it was hot out and give him some space. At that point I backed off and went to take some home video of the rest of the family and, out of nowhere, he sucker-punched my son." " - that seems to me like the dad had seen Tigger put his arms out to pose and tried to get into the picture himself. Since Tigger didn't kow he was there, the dad blindsided him.
Sort of interesting that a few minutes later, Jerry Jr seems to be doing what his dad did (blindsiding Tigger and messing with his head).
And, my last point - the dad is reported as saying that the handler apologized right away and said "Tigger was not feeling well today". That doesn't ring true as something said directly to the family or as part of an apology.
It DOES make sense for the handler to have said something like that to the other people who were waiting for Tigger (Mr. Monacho said there were 2 or 3 other people waiting). The other guests had been waiting for Tigger, were expecting to see Tigger and then suddenly, Tigger left (after those kids had seen Tigger's arm hit Jerry Jr and seen Jerry Jr
punch Tigger. The performer said in his police report that he had gone off after the incident to re-adjust his costume head. It makes perfect sense for the handler to explain
that by saying to the other people that Tigger was not feeling well.