The current pandemic situation aside, walking the Oirase is one of the more difficult logistical challenges, but you can be rewarded with some of the most beautiful scenery. The big problem is getting there and where you want to end up in the end. There are buses you can take, but they are very few only about 3 going there per day, plus only the first two will let you make it a day trip. The other option is renting a car, but one way down the whole Oirase is 14 km, so that means walking back to your car, and I sorely doubt your kids would be willing and able to walk 28 km in a day. Plus the bus from Hachinohe to the Ishigedo bus stop one way is about 90 minutes.
The bus is your best choice. But there are only 2 buses in the morning - it pretty much means that if you want to do the hike and get the first bus, you will need to stay in Hachinohe the night before to catch it. Of course, after the hike, if you plan to stay overnight at Lake Towada, go by bus to Aomori, or return to Hachinohe matters a lot as well. You may be able to get the 青森･八戸･十和田湖フリーきっぷ (Aomori Hachinohe Towadako Free Ticket) to save some money on the bus fare. Ask at the JR office or Tourist Info Office in Hachinohe or Aomori.
It is one of the most unforgettable places you will ever see. But it does take a lot of planning to avoid any potential migraines or disasters.
Hello, I just wrote an answer to the different question about visiting Oirase Gorge in winter. You can check out from here (https://hubjapan.io/questions/hi-all-please-help-us-to-enjoy-the-oirase-winter) if you are interested :)