Are you on the island 7 days/nights?
what is your accommodation budget?
Do you want/need a pool for the child?
Can you afford resort hotels, or are you looking for budget modest pricing.

Reason I ask is we have budget accommodation here but the quality ranges widely. Mostly you get what you pay for. So if you can afford nicer, we can suggest the better places and then suggest an itinerary.

I agree you will be better served driving during the daytime to get the most out of the scenic roads. Also, there are 3 ways to get to Volcanoes NP from Kona. All of them scenic and special in their own way. You can't go wrong.

For example:
If you were to spend your first night in Kailua-Kona, you could dine at the Kona Brewpub. Micro beers, excellent pizza & salads, and micro-brewed sodas for the kids. Walk around Kailua town & get good & tired for your first sleep. Then the next morning at day break you can head south out of Kailua and after passing thru the funky village of Captain Cook look for the Manago Hotel on the right. Stop in there for the famous breakfasts. Then continue down to Place of Refuge for your first "tourist" stop. A national historic park. Check out the ruins and hopefully a sleeping turtle on the beach. After that continue on the southern route that takes you eventually all the way to Volcano, passing many scenic views, optional spur detour to South Point, Punaluu Black Sand Beach (more turtles) and more small funky towns. Have your passenger keep a lookout on the water, there may still be whales around (slight chance). You can pit stop in Na'alehu for a bathroom break, cup of coffee, lunch etc.

If the trade winds are blowing normally, I would not recommend this route unless you get an early start. Later in the day the vog starts to really build up and it will hurt the views, diminish the experience, etc.

So there's just one idea...

I would recommend the "The Big Island Revealed" guidebook as a reference.