We’ve had our summer 2 week family holiday in the Tyrol for the last 4 years, tho lad is a bit older – now 15. 2 locations, a week in each.
Ellmau is next village along from Soll. Nice enough, though not the best location.
Bearing in mind the children’s age and your preference for flying, I’d recommend either Mayrhofen, in the Zillertal, or Seefeld/Leutasch. Latter is very chilled. We stayed at the Hotel Xander in Leutasch which I’d thoroughly recommend.
We were in the Stubai and Oetz valleys last year. Stayed at Hotel Erhart in Soelden, Oetztal, which again I’d thoroughly recommend. Made a great base for exploring the valley. Some fantastic walking out of Obergurgl up to the glaciers.
You can use someone like Inghams for flights, accommodation etc., but we tend to sort it all out ourselves direct. Much cheaper. All aBove are easily accessed by public transport from Innsbruck, are nice towns in their own right and certainly have enough to keep you occupied for a week or so at least.
If you’re looking at hotels remember that many provide a local travel card foc for valley buses, swimming pool/spa and cable car discounts.
Hope you can work something out – have a great time.