Not exactly…. The police segway lady was a part of the Alex-lighter-grandma arc of the episode. She showed how Alex always follows the rules, juxtaposing that with her rebel sister, Haley…. The letter that Phil's mom wrote to Alex included something like "Don't be afraid to break the rules, it's how I met Grandpa"

Well I'm a year later to the party than you are, but the answer to your question is, she was a part of the Alex-lighter-grandma arc of the episode. The pool security guard lady was there so show how Alex always follows the rules, juxtaposing that with her rebel sister, Haley…. The letter that Phil's mom wrote to…