S.R.
I don't think it's tacky at all... if you aren't sending out gilded invitations or anything. I mean, it's just family. Spread the word verbally that you are going to dland that day to celebrate your daughter's birthday, and anyone is welcome to plan their own disneyland trips for that day too if the time is right for them. Make it low-pressure, disneyland is very expensive with a family.
I know in my own family, we love to get the cousins together, and if one family was going for their kids b-day, we would probably be more than happy to join in and pay for our own trip at the same time just to make it a party and a memorable experience for the kids.
I just don't think you can send out any formal kind of invite for this, because then that implies you are hosting. You just have to tell folks that you are taking her for the first time and that anyone from the extended family is welcome to join up with you at the park. Also say that you totally understand if they aren't in the market for an expensive all day trip to the theme park at this time. I don't know anyone who would assume that by saying it that way you are planning to pay their entrance fees.