This was rude...right?

It's been a rough couple of weeks. My 8 month old had surgery about a week and a half ago. While she was in the hospital, we missed several appointments for my other kiddo, so this week we are playing catch up. I'm not sleeping well because my infant keeps waking up 3-5 times a night since we left the hospital. I'm overwhelmed.

My friend knows all of this. And she's usually super supportive. But today...

I had an appointment for my toddler an hour and a half away. The appointment was for 10:40, with a 10:25 check in time. My toddler had a leg surgery a year ago and her leg is still like spitting out some stitches and causing pain for some reason. This is the FOURTH time we've made a trip there and paid a $40 co-pay just to spend 5 minutes plucking out a stitch.

I spend my morning rushing around. Feed the kids. Get ready. Get the kids ready. It's stressful because my infant is still healing and my toddler is potty training. My toddler insists on wearing underwear for the car ride. Sigh.

We have to stop and get gas because I forgot yesterday. I didn't have time to make coffee, so we grab that too. We get to the hospital 15 minutes before the appointment. My daughter is dry and she pees in the potty I keep in the trunk. We get through security and up to the clinic. They call us up to the window. My infant is hungry and fussing and my toddler is whining.

They say, "Miss, are you aware your appointment was at 9:25 this morning?" With an attitude.

I lost it. I immediately started crying. I say, "I'm so sorry. I wrote it down incorrectly. Is there anything you can do? We just drove so far and this stitch is really bothering my daughter. These appointments are so fast, can they try to squeeze her in?"

The lady is rude, but asks the nurse to check. They agree to see us.

I tell my friend. Her response: "Yeah, well they have a schedule to maintain. It's not her fault you missed the appointment. I'm glad they're seeing you, but she had every right to be rude. I get yelled at everyone for other people's stupid mistakes."

Wait, what? First of all, no one ever has the right to be rude to someone, especially at their job. Secondly, it wasn't a "stupid" mistake, it was an honest one. And the woman could have said they wouldn't see me, and that would have been that, but she could still be polite.

She went on about how they have families to go home to too. I get that she works at a hospital, but I just felt like it was rude. I understand she can see both sides, but logic isn't always appropriate. Like if someone is struggling, just validate their feelings. Is it so hard to say, "Oh no! That sounds like a hard situation. I'm glad they are agreeing to see you." Like why contribute negativity?

I just felt like it was really insensitive. She knows everything I've been going through. Sigh.

Edit: It's hard to relay tone and facial expressions. Trust me, she was rude. And it's certainly not that I can't empathize with her or respect the schedules, but it was an honest mistake and my daughter was hurting. I just feel like as a friend you support your friends when they need it, and then throw the logic at them later.