I think stuff like this could easily be avoided by coordinating with the secretary's staff beforehand, "Hey, Secretary Noem's coordinator, I'm Senator Padilla. I'd like to ask the Secretary some questions at he press conference."
And if the Secretary's assistant says, ""Sorry, the Secretary won't be taking questions at that time," then Padilla can set up his own press conference immediately after or better yet, before the Secretary's to feed the press relevant questions, so they can ask.
Just showing up, interrupting the scheduled event, and then yelling "I'm Senator Alex Padilla" does not give the Senator carte blanche to interrupt the scheduled event. If it did, then you'd see lots of folks showing up at events and yelling, "No, I'm Senator Padilla. Now, let me do whatever I want!" Then others would show up yelling, "No, I'm Spartacus!"
The security for the event saw an unscheduled interruption, some guy telling the security detachment that he was Senator Padilla (without documentation), and yelling and scuffling with security. Of course, you take this guy out of the room away from the Secretary and if he is physically resisting, you secure him, with handcuffs if necessary, and then investigate who he is and what he is trying to do.
I do not see a problem with that at all. Just showing up and yelling so you can get video of the Senator being handcuffed is grandstanding.