It isn’t possible to tell by your profile where you are, but if you do a search of local gyms you can check their sites and/or call to ask about policies. Although your ability to come with your daughter is an important factor, please spend some time thinking about what other factors are important to you: For example, what hours are you most likely want to get there? Even if they let your daughter in, if the hours you could arrive are when they are closing, or if they have policies on the hours she can use it that may not work for you.
Most of the Ys with which I am familiar have a tiered youth program. At a certain age you take a class, and then have access to certain activities/equipment, and at different levels more things become available. I think it is a good system, as before a certain age bones are still developing and lifting heavy weights may not be helpful. They are not, however, the only gyms to have such programs.
A club with a pool will often draw families, and so is likely to have a robust program for children/youth. But again, you want to consider what activities you wish to do together. That is another list to make before you start calling around. No point joining a place with racquetball but no zumba classes, if you really want to do zumba.
Good luck, and congratulations on making a decision to do something healthy together.