I did a trip similar to this a few years ago in April, albeit without kids (high on my list to get my 12 and 10 yo out there).
We went in the reverse order, but here was our itinerary for what it’s worth…if Big Bend is the main draw and the rest is ancillary you’ll want to nix a lot of this.
While High Plains’ post above is great, you’ll have to pick and choose. All of his suggestions are great, but would take a lot longer than what you have to properly experience.
Day 1: Austin to Fort Davis; stayed in an Airbnb above the drugstore/restaurant; Late night star party at McDonald’s Observatory.
Day 2: AM Fort David National Historic Site and Davis Mountains State Park hike; There are some pretty easy hikes you can do in Davis Mountains but in June, you’ll want to start early and hit the historic site after. It was interesting but not a must do. I think there would be enough to keep your girls interested and it not be a complete bore (regardless, shouldn’t take more than an hour or 2). I seem to recall they had several “walk in their shoes” exhibits that did a good job showing what life was like on the West Texas frontier in the late 1800s depending on your circumstance in life (officer, officer’s wife, medic, etc). PM we drove to Marfa, checked out whatever shops were open, found a bite to eat, and stayed the night there.
Day 3: Drove from Marfa to Terlingua via US 67 to Presidio and SH 170/River Road. Your girls may not fully appreciate it but highly recommend that route for the scenery and the “is this really Texas? In the middle of a desert?” vibes. We stopped and did the Closed Canyon Trail in BBRSP which the girls might love (fair amount of scrambling from what I recall). After that drove in to BBNP and hiked Saint Elena Canyon (started the hike around 5, which probably won’t be a good idea in June, but as stated above, the canyon walls should provide some decent shade.
Day 4: Up early to hike Balanced Rock. Headed back home via 385/Marathon. There is a Fossil Discovery Exhibit on your way out of the park that, after looking at pictures online, I wish we had stopped to check out.
Again, the actual Big Bend NP part of this trip was relatively small. There was a fire that had just started on the South Rim when we were there and they closed the Chisos Basin so I think we had to scramble to make alternative plans.
Coming in to Big Bend NP and ending in Fort Davis, you might do well to:
Thu PM: hit Big Bend NP through Marathon, check out the Fossil Discovery Exhibit, and Balanced Rock (the two are super close as the crow flies, but unfortunately a 45 minute drive (then again, so is everything in that part of the world).
Friday: Chisos Basin (Lost Mine or Window View Trail) and Santa Elena Canyon. Rio Grande Village (Rio Grande Village Nature Trail) is great for sunset but on the opposite end of the park and an hour drive back to Terlingua.
Saturday: Terlingua to Marfa/Fort Davis via River Road. Stop for morning hike at Closed Canyon in BBRSP. Drive on to Marfa. Stop for lunch at Bordo’s (closes at 3). Let the wife and girls toodle around whatever shops may be open while you head to Marfa Spirit Co. Head on to Fort Davis and get settled in to your AirBNB/rest before star party.
Sunday: I’m usually one to pack up, grab a light breakfast and hit the road, but if ya’ll are on a more leisurely pace, this would be the time to check out Balmorhea State Park on your way home. Or if not into swimming, check out Fort Davis National Historic Site. And if absolutely jonesing for more hiking, a couple of options: 1) find a short hike in Davis Mountains State Park, or 2) head home through Alpine and do the short hike up to the Sul Ross Desk behind the Sul Ross State University campus.