I don't know why they would even have a captain at 11. That's unnecessary pressure in my opinion, and it would be a very rare 11 year old with the confidence to show any real leadership. Your daughter would not be unreasonable in saying she doesn't want to do it if it's creating stress for her.
The coach sounds like the kind of jerk youth football is trying to get rid of. Unless she is behaving badly in some way - stropping, fouling, dissenting with the ref -- there is no reason to give your players grief. They want to win as much as the coaches do and are doing their best. It's pointless to yell at them for having an off day. All it does is knock their confidence, and they need that confidence to play better next time.
I'm not sure if she is playing on a girls team or a mixed team, but either way if they are getting beaten every week then they are in the wrong league or division. The coach needs to support them through this until they can get in a more suitable division.
As for the coach, I think you should start speak to the club's Club Welfare Officer about him. Every club has a Club Welfare Officer and they are the first person to speak to if you think the coach is acting inappropriately. That includes situations like this -- it doesn't have to rise to the level of abuse. If a coach is just using poor practice you should let them know. Check your club's website for the Child Welfare Officer, or ask the Chairman or Club Secretary who it is. Your daughter's coach should have had FA Level 1 training at minimum and should know better than to act like that.
Can you find a team with a coach with a better attitude? Maybe a team in a girls-only league? I don't think there is that much of a size difference at your daughter's age, but a lot of girls prefer playing in a girls only league, because who wants to carry the weight of expectation for your entire gender when you are just trying to have fun playing footie on a Sunday morning.
But to answer your specific question, no you are not being unreasonable. I've been a footie mum for 12 years. I run a small football club myself and sit on the committee of another much larger club. I am a Welfare Officer, too. And this coach is out of order.