If you can't make Glacier, the Badlands and Custer SP are worth a trip in and of itself
In view of your available dates I agree with my friends above. We spent a week in Custer (Custer's Gulch Campground--private) and had access to Custer State Park, Wildlife Loop, Needles Highway, Iron Mountain Road, Rapid City, Deadwood, Crazy Horse, and Mount Rushmore (to name some highlights).
One of our favorite campgrounds is Mountain Meadows in Hungry Horse on the west side of Glacier, but that was in high season when Road to the Sun was fully open. That's where I'd go back for a Glacier visit, but only when the park would be fully open.