Suggestions on Jefferson - St. Charles Itinerary with 4 year old

If it's not too much trouble, we'd be interested in feedback from veteran Katy Trail bikers on our planned itinerary. Here's the plan:

Day 1
Drive to Jefferson City - ideas on where to stay?

Day 2
Start at Jefferson City, leaving car at Amtrak Station
Ride to N. Jefferson, hitting Tebbetts, Mokane or Steedman for lunch
Finish at Rhineland for night, possibly staying at Les Lavandes
Total for day: 41

Day 3
Ride to Treloar or Peers for lunch
Visit Blumenhof Vineyards in Dutzow
Finish at Augusta for night, hopefully with ample time to visit several wineries - recommendations on where to stay? Not seeing many places that would allow a child and perhaps have a hot tub.
Total for day: 39

Day 4
Ride to Defiance to visit Yellow House
Possible picnic lunch stop at Weldon Spring or further along?
End early at St. Charles in time to sightsee and visit wineries
Possibly stay Country Inn on Main Street unless we can find a good inn or B&B ok for our daughter. Would also appreciate input on things of interest for kids in St. Charles
Total for day: 27

Day 5
Take shuttle from St. Charles to Kirkwood, eat lunch/spend day
Ride train from Kirkwood back to station in Jefferson

Questions:
Suggestions on where to eat and stay, what to see along the way
Is this a reasonable distance (27 - 41 miles/day) to cover daily at a leisurely clip with plenty of stops?
Ideas on keeping kiddo busy during the ride? She's well-behaved and will enjoy it, but any unique ideas are welcome.
General comments?

I realize this is a lot of information, so thanks in advance to anyone plowing through it to make suggestions!

In Jeff City, staying at the Capitol Plaza (I think that's the name) would be good as they have an indoor pool. And there are eating places within walking distance (pizza is good). To get to the trailhead you take a cab as the ride there is a challenge especially if you have a trailer. From there to Rhineland should be a good ride. It takes longer to cover that much mileage with a trailer especially when you are stopping. Make sure places are open because that is always an issue, especially on Mondays or Tuesday. I don't know anything about the place you propose to stay in Rhineland.
Finishing in Augusta - many nice places to stay its the child that may be a challenge. There is one B&B that has a guesthouse that might really be good. You are across the street from the B&B but its very cozy, little kitchen, quaint and quiet. I've forgotten the name but its in the Guidebook. St. Charles should have plenty to keep you busy. Street entertainers during the summer months. Shops. Food. There are B&B's but there is a large hotel - maybe a Embassy Suites - not far at all. Indoor pool I believe and free breakfast. And the rooms are designed well for adults with children. Your mileage sounds about right with a 4 year old. Take snacks along - that's what I did. You should have fun.

I'd check this website and contact hotels in Jeff City about offering to shuttle you across the river bridge. Although I've ridden it before, I wouldn't do it with a child. The Complete Katy Trail Guidebook by Brett Dufur is a must have reference. It highlights many points of interest such as side trails, conservation areas, historical information, etc. that may be of more interest to a 4 year old child than visiting wineries. I'd save those for an adult trip where they could perhaps be more fully enjoyed....but I'm not a window shopper at the wineries.

I think your daily mileage is doable so long as the trail has not had any rain before you ride it. I received a trailer for Christmas and decided to take my granddaughter (7month) out for a test ride those few days we had 60+ weather lately. I was surprised at how much the wet trail affected my speed, I was struggling to make 5mph in those spots where there was a dip in the trail. More water had accumulated in those spots making the trail considerably softer. After about a mile or so I called it quits and had my wife pick us up.