A Reasonable Routing and Timing
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Since you and your husband have such different attitudes towards RoadTrips, it will be important that you find a middle ground that works for both of you as well as the child. That means a minimum of six days of driving. Your husband might be able to do it in less, but you'd be uncomfortable and the toddler would be miserable.
The shortest route would be to get on I-15 north from wherever you are in the Los Angeles area up to Barstow where you'd get on I-40 east and continue all the way to Oklahoma City. There take I-44 (toll in OK) to St. Louis. Cross the Mississippi and do a short stint on I-55 to I-70 eastbound. Stay on that until it joins I-76, the Pennsylvania Turnpike (toll) into the Philly area. Depending on the time of day and your familiarity with a particular city, you may want to use beltways or bypasses rather than stay on the main Interstates which tend to run right through the heart of downtown. Cities where you might want to consider this include Oklahoma City, St. Louis, Indianapolis, and Columbus.
If your main aim is to make the trip in a reasonably short time, then I wouldn't be looking at any major detours to attractions such as the Grand Canyon which could add the better part of another day to your trip. But you should certainly make a little time each day for two or three short stops to let your child get a little fresh air and exercise.
AZBuck
