Emergencies and the Four-year-old Girl

The police came to my door yesterday afternoon.
Apparently, in my efforts to teach Lily about emergencies and dialing 911, I accidentally called the police department for real. So when the officer came to my door, I sheepishly explained what I was trying to accomplish. The understanding cop smiled and said, "So, is everyone all right?"
"Yes. I'm so sorry," I said. I looked at Lily.
"Are we all right?" I asked her. She nodded. "See what happens when we call 911? The police come and make sure everything is all right." She nodded again, smiling.
"I'm so sorry," I said again to the cop.
"No problem."
What I wanted to tell the nice policeman was that everything was not all right. What is wrong with my daughter? Every time I try to explain something important to her, she just doesn't get it. This lesson went better than this attempt to teach her not to go with strangers, but it did not go well.
I spoke to Lily about emergencies and told her they may be a time when Mommy or her grandmother might fall down and can't get up, and she would have to get help. "Let's pretend I'm hurt and can't get up," I said.
"Okay!"
I fell to the floor and lay there, not moving.
"Mommy!" said Lily. She was laughing. I didn't move.
"Mo-mmy!" she sang. "Get u-up!" I stayed still.
"Mommy!" she yelled. “Wake up!”
This isn't working, I thought.
"Lily, you're supposed to ask if I'm all right."
"Oh. Are you all right?" She smiled down at me, putting an arm on my shoulder.
"No!"
She pulled her arm away and stared at me.
I sighed. This was going to be harder than I thought. I have no fricking idea how to educate children, nor do I have the patience.
"Listen, Lily. There might be a time when Mommy or someone else gets really hurt, or if there is a fire, and these are called an emergencies. When those things happen, you have to quickly go and get the telephone."
"Now?'
"Yes, now. Go and get it."
She ran to the guest room and brought me the cordless phone. (I noticed her nails needed trimming, so of course, I started thinking about cutting her nails and not concentrating on the task at hand.)
"Okay, now here's the deal. If ever there is a time when Mommy can't get up, or your grandmother or a babysitter, you should first ask them if they are all right.” I showed her the buttons on the phone. “If they can’t answer you, pick up the phone and dial 'talk,' then 9-1-1. Can you do that?”
She nodded enthusiastically.
"Okay, show me."
She pushed talk, then 9-1-1. I immediately hung up the phone. We did this a few times, and most times I hit the 'talk' button again before she dialed 911 so she wouldn't really get through.
Turns out that just dialing those numbers is all you really need to get a 911 operator. A signal was sent to the police department, and I received a call a few minutes later.
"Is this Mrs. D?”
“Yes?”
“Did you just dial 911?"
"Oh, no.” I could feel the blood rushing to my face. “Oh, I'm so sorry. I was trying to teach my daughter about emergencies and calling 911."
“How old is your daughter?”
“Four.”
"Okay, ma'am. But a squad car will be there in a few minutes. With every 911 call we have to send a car out."
"I'm so sorry."
"It's all right."
I was mortified.