I started bringing my kids when they where 6 years old.
That first year My oldest did the last 2 days with me. He is now 15 and he hasn’t missed a day of RAGBRAI since.
Four years old seems a bit young to get started, especially if you are planning to have them ride the whole thing.
I can’t say much about doing RAGBRAI pulling the trailer. We started with a double wide trailer behind a mountain bike, but by the time we started ridding RAGBRAI I had my eldest on the back of a modified tandem. My youngest joined us the next year on a Trailer Cycle that we pulled with the tandem.
I Highly recommend going the tandem route if at all possible. it is much more efficient and stable. The difference between [Trailer -> Trailer Cycle -> Full Tandem] is huge.
With that said, here are my tips.
Make sure that the kids enjoy being in the trailer. Give them things to do (we had a bucket of Legos back in our trailer days). Ridding should be something they look forward to and not something that they dread. It is very likely that they will be sleeping for a majority of the ride time. Find parks/playgrounds at your stops to give them a chance to play. Get them excited about the stops you plan to make that day and include them in planning those stops. My boys get very excited when they hear the 2-cycle engines and know that we are stopping for ice cream.
Make sure that you are physically able to pull the trailer on long hot hilly days.
Get Lights and Start Early. You will be stopping a lot, and stops will take significantly longer than ridding solo. Lines are shorter early in the day. The road is less crowded for your long, less stable bike. It also gets you out of the hottest part of the day.
Be prepared for the weather. Trailers are not water tight. Dealing with Heat is obvious, but you need to be able to deal with Cold as well. We were caught out on RAGBRAI one year with 60 degree temps and rain. I did not have enough warm clothes for the kids, and it was miserable.
Practice routines so that you can trust them to stay Hydrated. Remind them to drink and monitor their water bottles to make sure that they are.
Help them with bathroom hygiene. Young children don’t always do the best at cleaning themselves up (especially in kibos). It might be less important in a trailer than on bike saddles, but chafing and skin irritation can be serious trouble. I always used to carry an extra strength tube of diaper rash cream to use as a preventative after bathroom stops.
Sun protection is incredibly important. Apply sunscreen early and often.
Practice tent camping before RAGBRAI (if you have other arrangements, practice those). About a week before the ride, start waking them up early so it isn’t a shock when you start the ride. Also, work on staying quite in the morning. You will hopefully be up and out early and you don’t want to bother other campers. If they are able give them jobs in the morning to help break camp. Do as much as you can the night before to have camp ready to break. For us, breaking camp and getting started has been the most difficult part of the ride.
Swimming pools, Community Centers and YMCAs are the best places to get showers (short of having an rv or a charter with in camp showers). Most of these have “Family” shower areas. Often these have NO LINES. Many of these places also have a lower admission rate for children so you can save a few bucks over a shower truck. Choose an Indoor pool over an outdoor pool to avoid additional sun exposure. My boys love swimming and very much looked forward to finding a pool.
Expect them to get whiney and have an idea of what you will do when it happens (35 + hours in a trailer is a long time)
Overall, Practice and Routine will make the biggest difference. Something is bound to go wrong, and how you deal with that could impact the kids future desire to ride with you. Don’t be disappointed if you have to bail. Four is very young to be doing more than a day of RAGBRAI.