Jwar, you are brave for putting your struggles out there. Sounds like a lot of us have some issues too. Comiserating can be helpful to a point. Sometimes it is easy to offer a suggestion from another view, maybe some things we can't see due to the fog of war surrounding our brains.
Suggestions for daily activities can be tough, getting out of the house almost always costs money, which also seems to be a problem.
You are in KC, right? Weather is still too shitty here to do much outside, but visiting playgrounds, parks, lakes would be fun when the weather warms up. Plus free. Also the time of year that going to a frozen lake wouldn't work either.
There are a couple of indoor playgrounds around here. One is free at the mall. Or even McDonalds or Burger King. Let the kid run around while stuffing your nugget hole with nuggets. Or not. Unhealthy food though, obviously. But I love McDonalds breakfast or even just coffee. Seriously never eat that stuff myself, due to already being a semi-fat fuck as well as monies.
How are the public libraries near you? Some might have an interesting kids section. Maybe make it part of a weekly routine where you go and read a few books, and take a few home.
How is the local zoo? Season family passes might not be terribly priced, might be a fun place to hit every few weeks and get some exercise while letting your daughter have some fun too. There are plenty of indoor exhibits here, but Henry Doorly Zoo is pretty tops, not all zoos are equal. During the work week is the best time to avoid crowds too.
Do you have a gym membership? Do they offer swimming lessons for kids? My daughter was about that age when she started swimming at a local gym that my parents were paying for. When we got slow at work I was taking Wednesdays off to take her to the lessons, which then resulted in her making me get in the pool after the lessons. Then she insisted on holding on to my back while I swam laps for fun. Great bonding.
What is this Kids Club thing? Like daycare? This might be one of those things where you have to lay down the law and be the one in charge by insisting she go. Kids are pretty adaptive, she might stop complaining after it becomes a regular routine for her.
Daytime bowling could be a blast with bumpers.
Your role in your daughters life is tremendous to her development. Don't ever be ashamed of staying home or underestimate your importance in your family.
Try to arrange some date nights with your wife. Your relationship is important too. A modest evening out for a few hours, even just dinner, would help you to stay connected to each other without the little ones demanding your attention. It can be hard too. On the rare occasion the wife and I go out we often end up talking about our girls and how much fun they are likely having with their grandparents and/or cousins. We tend to make it a dinner and concert night too. Getting her out to talk to my friends helps her too since she is a stay at home mom.
Hope something here helps man.
I really, really hope you can come to our little get together in August. You and Ben are such inspirations to me and I love hanging out with him, so I'm sure the same would apply for yourself. 
