do shell script "open -a \"/Applications/Firefox.app\" '" & yourUrl & "'"
It may very well be that FireFox somehow violates the normal application architecture, I’d also try to remove any installed plugin and retry if it doesn’t work the first time around.
If the open command doesn’t work, then that is a signal that the current version of Firefox doesn’t respect the events it is supposed to respect, and I’d move on to Chrome or Safari.
The fact that Firefox has an AppleScript dictionary means next to nothing.
It happens to have the default AppleScript dictionary with NO Firefox AppleScript Suite, therefore you can do something like get and set window bounds - but you cannot interact with the app in any meaningful way.
The Firefox people decided that AppleScript was a security threat and canned the Mozilla Suite years ago.
Shame on them. I would use it if it was scriptable. As is I keep it for testing and for the occasional use of some of the handier plugins - but I use Safari for my everyday stuff, specifically because it is scriptable.