I'm sorry for the loss of your husband. I take it this will be your first trip to Europe.
First, check out some guidebooks from your pubic library for the countries you mentioned. Some, like the DK series, have lots of color pictures as well as information. Others include the Fodor and Frommer series, Lonely Planet, and the Rick Steves guides. Read about the places you want to visit, logistics of getting there and around, and lodging options (which of course are much broader than just those listed). You may want to invest in the latest versions of the guides that seem most useful to you; those in the library may be a few years old and things do change. Also, buy or borrow Rick Steves' Europe Through the Back Door. If you have a Kindle, it's on sale for $1.99 right now, a great bargain. Full of information on the practicalities of getting to Europe, getting around, staying in cities, and experiencing Europe as more than just a museum or food fest.
With 35 days you can choose cities or sights in all three countries, keeping in mind that you won't be able to see "everything" but hoping that you can see more on future trips. Try to fly "open jaw," for example from Minneapolis to Rome and returning from London to Minneapolis, or vice versa, so you don't spend time and money backtracking. You may want to start with Italy and finish with UK simply because of weather, Italy gets hot in summer and earlier may be a little cooler. Or, depending on your language skills, you may want to start with UK where they speak (more or less) your language. But don't feel constrained, with a few French and Italian phrases you should be able to function.
If I were planning a monthlong trip I'd try to spend about five days in each of six places, to minimize packing/unpacking and travel time. Consider that every time you move takes at least half a day, or maybe a whole day. Several days, or even a week, in a city give you a chance to know it better, feel comfortable getting around, see what you want to see, and take some down-time that even your high-energy daughters may appreciate.
It's good that your daughters are old enough and open enough to new experiences. The more you can involve them in planning the trip, the likelier you all are to enjoy it. This means compromises. One strategy is to give each person a day to plan in each place you visit. Another might be to split up for a morning or afternoon or evening once in awhile, letting the girls (together) do something they want while you do something you want (a nap, perhaps?).
I could go on, but Europe Through the Back Door says it better. When you have a more focused idea of where you want to go and how, you can get a lot of help on this forum from some very experienced, kind, and helpful people. But it'll be your trip, not theirs, so put your own choices first. For a July trip it's definitely time to start planning, which for many of us is half the fun. Good luck and happy travels.