I am amazed at the parents who pull their kids on RAGBRAI. A week of tent camping with toddlers in a different town each night would be exhausting, nevermind the 50-80mi rides each day before camping.
We used a burley for our first kid and for the first year of our second kid. They are fine, but are basically bubbles and make it tough to interact during what should be family time.
We bought a used Weehoo trailer and that completely changed family rides. It lets the kid be involved in conversation about what you see, where you are going, etc. The single wheel made for easier turning, took up less width on trails, and was also easier to store.
Regardless of what you use, itll be heavy and make you ride slower. Wind resistance is higher. Weight your legs are propelling is higher. You are just slower.
Perhaps adjust your approach and dont focus on speed, but rather on experiences(parks, playgrounds, libraries, ice cream, etc).