One thing to keep in mind--kids can generally sleep anywhere. And, with kids that young, my guess is that you are still young too. Many of us on this forum who RV in Alaska are no longer your age, so keep that in mind when reading these responses.
In early July in south-central Alaska, the sun will not go down until 11:00 pm and will come up at maybe 2 or 3:00 am. So, with a motorhome, you can put the kids to bed and still drive in daylight/dusk until very late at "night." When our kids were that young, we put them to bed in the back seat, or the back of the station wagon with the seats folded down, and drove all night to a relative's house by alternating drivers. As long as you get enough sleep to drive safely, you should be able to cover pretty long distances in a day, even by Alaska standards and even over Alaska's never-ending road construction.
Just as an aside, when I was working on environmental cleanup projects at Elmendorf AFB in the early 1990's, we normally worked 10-12-hour days. A number of the Alaskans who worked with us would work all day, then take off for the Susitna River at 6:00 or 7:00 pm. They would fish all night, then get home in time to shower and change clothes before heading back for another 12-hour work day. On weekends, they would tow their boats to Seward or Homer and fish all weekend for halibut and get home in the wee hours of Monday morning. And, during dipnet season on the Kenai River (for Alaska residents only), they would take 2 or 3 days off to restock the smoker and freezer with reds. When asked about doing all that fishing all summer long, their stock answer was "I have all winter to catch up on my sleep!"