I expect--I SINCERELY HOPE--that you will be fine by the last of June. But I would certainly check with the campground as there may be lasting effects in particular areas.
We have stayed at Treetops RV and Dallas Metro KOA, both in the Arlington area.
In the same general area we have stayed in Cedar Hill State Park. If you generally prefer (as I do) state park settings that would be a good choice.
These may not be in the area of Dallas which would be convenient for you, but these are the ones we have actually stayed in and would recommend.