I agree with the comment above about having your daughter go to the mall security office and asking for an escort to her car. If they do not the mall may be liable for at least allowing an unsafe work environment for their contractors employees. I have NEVER been refused an escort request; actually, our facility security have asked if I needed an escort.
IF they refuse, and someone gets accosted on their property, they (the mall) are setting themselves up for a lawsuit.
As to the request to leave... sadly, the guards were well within their rights. It sux, I know, but if they ask you to leave, then leave you must. But again, TELL YOUR KID to stop by the security office and ask for an escort. Remember, just like your limited police powers at your contractee (place wherre you do security), they have the same right, and are likely following their company and contractee's written orders. If they didn't, then were I their supervisor I'd fire them, no matter how unfair.
OTOH, re YOUR employer firing you... absolutely no way. You might get a talking to about putting our company in a bad light to the mall (and the competition) but I would understand your motives, and would prolly give you a pass as long as it didn't happen again. Bottom line - escort your kid plainclothes as a private citizen, carrying concealed if you must (as long as you have a CCW) and if SHTF you can use your "profrssional experience" before a judge (or ore likely, with the cops you may already know as part of your job)...
Remember, the SO's at the mall are just like you-paid to enforce their clients rules and regs. If you're not a contracted SO at the mall, you maybe should shun your uniform first? We had a strict policy against going to another company's client's place of biz in uniform when I did SO work... just remember, you wouldn't like a stranger poking around in a competitors uniform at your client's POB...