A 'Round Trip' from Almost Anywhere
OK, It looks like your trip is starting to firm up. So at this point you should be looking, I think, for a basic backbone of your RoadTrip that lets your wife and daughter fly into whichever airport works out best for the three of you, see as much as you comfortably can of northern New England, and finally return to St. Louis. So, assuming you'll be flying into one of the airports that have been discussed so far, what might such a drive look like?
Your initial goal should be to get to Portland, whether to pick up your family or to start the main portion of your trip. If they fly into Syracuse, Albany or Hartford, then you might want to head for MA-2 across northern Massachusetts to I-495/I-95 north. If your family is with you at this point, there are some nice beaches along the New Hampshre coast including Hampton Beach and Rye Beach. Next up is the quintessential New England lighthouse in York, ME. And things just get better after Portland.
Using I-295 out of Portland to Brunswick would put you on US-1 along the 'rock-ribbed' coast of Maine. As i noted in my initial response, there are a few less-visited peninsulas northeast ('Down East') of Portland including those leading to Boothbay Harbor, South Bristol, and Pemaquid Point. Of course, the more popular distination is Acadia National Park, which for you might mark a turn-around point for heading back through inland northern New England.
From Ellsworth, I'd suggest looking at US-1A to Bangor and then US-2 into northern New Hampshire. There a drive to the top of Mount Washington would be in order. In Jefferson NH there are a couple of small amusement parks that would be perfect for a young child. Continuing west, you should consider driving to/through Stowe, the Trapp Family Lodge (the Baron and Maria von Trapp are buried in a small private cemetary on the grounds), and Smugglers Notch ending up on the shore of Lake Champlain.
Now, depending on how much time you have to get back to St. Louis, you can either take a 'direct' route such as I-87/I-84/I-81/I-80/I-71/I-70, or you could continue taking scenic roads and visit Gettysburg, the Shenandoah Valley, New River Gorge and Mammoth Cave.
But, again, that's just one possibility out of many.
AZBuck