Feel free to share my story with your husband. Maybe it will help him find a different way of approaching your daughter and sports.
When I was young, my father was the same way with me. He was a former college athlete and very competitive. I actually had a lot of athletic ability but his approach towards every sport I played took all of the fun out of the game for me. I could never get "in the zone" so to speak because I was always thinking about what he would be thinking, how I didn't try hard enough, run fast enough, go for it enough. I was always outside of myself rather than just being in the game. It just wasn't fun; in fact, it was stressful. Unfortunately, when my parents divorced when I was 14, I used his absence from our home as a way to quit all of it -- swim team, tennis team, soccer and more. This was too bad because high school is a time when sports are so great for girls ... for physical fitness, self-esteem, teamwork, college applications, etc. Today, as an adult, I thrive on my workouts ... I push myself to go further, run longer, etc, so I know that I've inherited my dad's traits. I regret that I lost the fun in athletics at an earlier age.
Try to encourage your husband to just let her participate. At 7, she won't get better because he pushes her, especially if she is already a little timid. He is probably trying to help her get past this timidity and develop some self-confidence but I'm not sure it's the right approach. Right now, just let her find her groove / sport / talent. Let her enjoy the camraderie and the physical activity. As she gets older, and is able to "self-select" a sport that she wants to pursue, she'll have enough confidence to take a little more pushing -- and she may need it at that time in order to stick with it which is important to learn too.
I hope this story helps ... not the perspective of the mom, but of the child.