Buy some guidebooks or check the catalog of your local library system and request some. Check google maps for any other appealing sites not listed in the guidebooks. You don't have to go to the most popular places if they are not appealing to you. Make a list of museums and sites that look appealing to you and your daughter. Type your list. Check google maps for opening and closing times. Check site websites for opening times not listed on google maps. Turn your list into a supposed day-by-day-itinerary. See what places need advance reservations. Make any necessary advance museum reservations. Edit your itinerary and type the times of your reservations. Do any museums in Paris need advance reservations? Make your hotel reservations only after you figure out exactly how many nights you need based on what you are seeing.
I spent 8 nights in London in July 2016. The authorities at Heathrow airport made me wait in the airport jail for over 3-1/2 hours until the lady responsible for doing this finally interviewed me and wrote 2 pages of drivel based on what I said and then took my picture and fingerprints and then I watched them search through my bags really completely; all because I took too long finding the information about my flights back to Detroit in my e-mail when I arrived at the passport-stamping booth, and I had printed my information and left it on my couch by my mistake. I am a bearded single man and atheist traveling alone if that matters. Carry all your printed information, reservations, tickets, and printed itinerary, in a rigid folder, or folded in half or thirds in a pencil case!
I have not traveled to any part of France yet. You probably could combine Paris and London in one trip.
In July 2017, I spent 13 nights in Italy, in Florence, Rome, and Naples. I didn't make time for Venice. The more cities you add, the less time you have for museums and sites. Many travelers probably just pick one or two museums in a big city and are happy to skip everything else. But instead of picking the number of nights I will spend in a place first and then randomly filling up my time, I would rather figure out what I will try seeing and then seeing how many nights I need in a place.
In London, I took the commuter train (it goes underground in many places and above ground in some places) to near my hotel and walked less than a mile the rest of the way. In Florence, I was able to walk from the train station to my hotel. There are local buses but I didn't use them but I wish I had.
With some effort it would be possible to buy all your tickets and make all your reservations without the need for a travel agent. I have never used a travel agent, but I also don't have kids to occupy myself with.
Search for prices for plane tickets for all the possible path you could travel in to see which makes most sense.
If you see just London and Paris, it would be best to start in one city and end in the other. I arrived and left from Rome because I that was the best flight I found. In Italy I took the trains between cities.
Have you considered just limiting yourself to England or France or Italy? If you fly between Paris and Rome or Venice, you will surely have to spend more time at the airports than at the train stations.
I have had good luck with most of the hotels I reserved on booking dot com. Competing sites include hotels dot com and expedia dot com.