I’m driving this route tomorrow with my three year old son. Looking for a place on the way to get fries and a beer our similar. He’s pretty picky when it comes to did but fries or pizza our similar work fairly well.
Portsmouth is about mid-way on your trip and has a bunch of great food and beer options. Portsmouth Brewery, Gaslight, Flatbread Pizza, Whym…
Good call. Gotta get off the pike for kittery anyway to visit the birthplace
Manchester/Hooksett:
White Birch Brewing (Rt 3 - Hooksett)
Milly’s Tavern/Stark Brewing (N. Commerical St. - Manchester)
Bert’s Better Beers - Beer Store ( Rt 3 - Hooksett near Exit 9 off of I93)
Portsmouth:
Earth Eagle Brewings - Gruits and Empyrial Ales ( 165 High St. adjacent to A&G Homebrew)
Portsmouth Brewery
Stoneface Brewing - Newington (Rt 4 just before going over the bridge)
WHYM (stands for Water, Hops, Yeast and Malt…clever huh?)
Throwback Brewery
Red Hook ( I know but an impressive facility)
*Avoid Thirsty Moose in Portsmouth. Over 125 taps but they know nothing about the beer or how to handle it.
On the way to Portland:
Banded Horn - Biddeford
Funky Bow - Biddeford (hard to find)
Portland:
Great Lost Bear - Forest Ave. There’s a couple beer stores on Forest as well (RSVP and Bier Cellar)
Novre Res - in the Old Port. Opens at 3 I think.
Of course there’s a lot more. Definitely go try Earth Eagle though. They are doing some really unique stuff.
Edit: just re-read you post about the 3 year old. I wrote these suggestions for your beer needs 
. Fat Belly’s in Portsmouth has a pretty good selection, burgers, wings, etc and a decent tap list).
nosh in Portland - Fantastic food and a small but good tap selection. http://www.noshkitchenbar.com/
Also if you are looking to browse some bottled beers, Carl’s Meat Market in Kittery is worth a stop.