I would make a visit to every single vet within 5 miles of your house...*really*. Take a flyer, tell them what happened and leave a flyer there.
Have your kids ask all their friends in the neighborhood.
Go to all school bus-stops within one mile of your house when the kids are going to school and also when they are coming home. Explain to any adults what happened with your dog. Hand adults & kids a flyer.
If your kids ride the bus, have them give some flyers to their driver, ask the driver to hand them around to other school-bus drivers at your kids' school.
Take a flyer in to the school office, ask to leave it there.
Report the missing dog to your animal control/police, I hate to say it but there could be a public safety issue here (possible wild animal/predator, people stealing pets, etc.)
My story about a missing dog is from my childhood. Our dog "Tawn" disappeared one day, we had no idea what happened. He was kind of a free spirit and was the jumping-est dog you ever saw, could jump straight up (kind of boing-boing y'know?) and could clear a five-foot fence if he wanted to. We had some land on the edge of town, horses, etc and for an animal to go missing wasn't unheard of. (We also seemed to take in lots of dogs that people just dumped out near us.)
So, anyway, about a year later, my mom gets a phone call. This lady said "we have your dog", my mom said "Oh, we haven't lost a dog in over a year, it can't be ours" and this lady said "well, he still has his county tags on and I called the Courthouse and it's your dog".
And my mom said ok I guess he's our dog and we'll come pick him up...
I was sick with one of the childhood illnesses we used to get...measles? mumps? so I couldn't go with her, so my mom & my brother got in our station wagon (remember those?) and drove to this lady's house to see if it really was our dog.
They drove up to the house and...
.
.
.
.
.
.
TAWN came running! He jumped up on the
top of the car, he looked down into the front windshield, then he jumped into the car through the open window... and my mom and my brother brought Tawn home. He lived for at least 15 more years, even moved with us and fathered a litter (sorry, it was a different time) of puppies in the spring before he finally passed away in the fall of his last year.
Now, you have to understand a few things here.
Tawn was in another
state.
On the other side of a *river*.
And he
hated to swim.
And the lady's house was at least 20 miles away from us.
He never would have gone or gotten that far of his own free-will.
My mom (who has always had kind of an ESP thing going) had a suspicion that a neighbor who HATED the dog had transported him north and dumped him somewhere up there, thinking he'd NEVER come back or that he'd just *die*. Now just imagine Tawn, trying and trying and trying to come back home and finally getting to that river and not being able to make it across...
And y'know what? I just thought of something...

I bet that neighbor was surprised when Tawn was finally home a year later!
I hope your family gets its own happy ending with your pup.
agnes!