First of all, I note you're going in June. If your date is near the solstice, Stonehenge will be more packed than usual. Are you thinking of going on the solstice date itself? If so, look up the English Heritage special advice for solstice visitors.
Assuming you'll go on a non-solstice day: if the Anderson tour to Stonehenge & Avebury gets an early start, that's a good sign because it probably means you'll have adequate time at each of the sites to enjoy and appreciate what's there. Stonehenge has a large visitor centre with exhibits indoors and out, and then it's about 1/4 mile to the henge itself. Not sure what your tour will have you do, but regular visitors can choose to take the free shuttle or walk. The entry fee includes an audio guide that you wear around your neck and its commentary is very good. The Avebury stone circle is a mile round.
If you don't care that much about Avebury, as noted by others you can do Stonehenge yourselves by taking the train from London to Salisbury. From there, a circulator bus will take you to Stonehenge and Old Sarum. If the teens want to stretch their legs, send them out to walk between Stonehenge and Woodhenge / Durrington Walls.
Don't rent a car for the one day. Navigating out of London and back would be a big headache, and if you took any wrong turns you could lose precious time at Stonehenge and Avebury. (Not that the countryside isn't lovely, but wandering around the Marlborough Downs wasn't what you came for.)
