Three times a week? For six-year-olds? This sounds like too much. I don't know any other sport -- and we're in a very sports-intense area -- other than football that has three weekly practices and/or games for kid that age.
You say you played as a kid. I bet you were good at it, or even played into junior high or high school competitively - did you? I wonder this because you seem pretty intense about it -- you find her "embarrassing" as if others' opinion of you somehow depended on how she (not you) performs. You say you "told the coach to ride her" and "I ride her myself." Ride her? She's six and this is for fun and exercise -- isn't it? She's having fun and acting, well, like she's six, and more interested in the other kids than in the details of the sport. If she weren't having fun she would let you know, but if you persist in trying to make her a very serious player, when she wants to go to see her friends, she will quickly burn out and lose any interest in this or any sport. Or she'll go the opposite way: Working so very hard to please you that she might grow to dread softball nights but keep going because it's what you value and expect of her, not what she enjoys. Please don't ride her to that point.
I'd just let her have fun for this season, and then next year ask her to try something different. I see too many kids who are put into one sport at age five or six and never, ever even taste any other kind of activity -- the one thing becomes their self-defining activity even if it's not what they might choose a few years later.
And parents sometimes think kids "should" be in a sport, as you put it, when they really don't. They need physical activity but it does not have to be a sport -- and it doesn't have to be the sport that you yourself did as a kid. She might focus better in another sport, or in dance, or gymastics, or on long walks with you and your family, or just having more playdates at the park since she is a social kid. She might never focus on any sport. If that's her, and she's active and healthy, you're still blessed.