Reserving for large groups isn't quite as scary as it seems. Pizzerias regularly accommodate big groups. It's an economical solution, but you do have to like noise ... Some restaurants have different rooms and are usually willing to give your group one. I've organized meals at Paris, in Trastevere, and Antico Arco, if you want something upscale. Checchino in Testaccio has a lovely private room upstairs you can reserve. Otherwise, don't be afraid just to call a trattoria (I seem to remember Lilli is quite spacious, but I haven't been there in a while). I believe someone I know used Fiammetta for a group. And do book well in advance.
Trattoria Luzzo near the Colosseum could handle groups your size. Its decent not great food, reasonable price. Osteria dell'Angelo, with Roman cooking, also has a couple of rooms and is family friendly. (in the Prati area, over by the Vatican)
Osteria dell' Angelo
Via Giovanni Bettolo, 24, Roma , IT
Via di San Giovanni in Laterano, Rome, Lazio 00184, IT
For Rome, I agree with Tavoleromane and would suggest Flavio al Velavevodetto.
I'd also add Gigetto, Costanza, Pompiere and Hosteria L'Orso 80.
All of these restaurants are very good, not touristy and have rooms big enough to accommodate.
Since you are quite a big group, it might be easier to agree to have, say, three different pastas for the entire table, that you can all have a taste of. (rather than each person ordering seperately) . The same can be done for the second courses.
Hosteria l'Oros 80 is fun, since they have a huge mixed antipasto, that arrives on the table as small plates to share. This is often almost enough to make up a meal.
And since you are such a large group you should (of course) reserve in advance.
Venice: assuming you are looking for restaurants that will have a menu that satisfy both adults and kids not expensive. For such a number, choices are limited. There will be tourists regardless where one eats; hopefully not 'touristy'. The following might work.
Alla Madonna: a large old style trattoria. No pizza but a large menu including many pasta choices, seafood as well as meat. I have not had good luck with the food but others on this board have had better.
Taverna San Trovaso, Da Aciugheta, Osteria alle Botteghe, Casin dei Noboli. These are large places with large menus: pizza, antipasti, pasta, secondi. Something for everyone.
If above places do not work, there are a few decent pizzeria in Venice. Besides pizzas, they will have a few antipasti, pasta and a couple of secondi. Try Nono Risorto, Dai Tosi, Birraria la Corte, Muro Vino e Cucina (a branch near the Frari and also one near Campo San Domini in Santa Croce: the main branch in Campo Bella Viena is not for kids).
If you are visiting Venice in the warmer months, there might be more choices since outside seating kicks in.
Most eating places are small and cramp. And their regular menu don't necessary have choices for kids. If you are interested in any of the places that have been recommended on this board, no harm inquiring if they can accommodate your large group (given if you reserve way ahead of time since you'll be taking up most of the space) and if they can do a menu for kids. Mostly lightly you will have to order from a limited menu and a set cost for your party.
Good luck! It will not be easy...
In Rome you can try to book at Flavio al velavevodetto or Da bucatino that have quite large spaces. Both are in Testaccio area and have traditional Roman cuisine. Please let me know if you are also interested in pizza or in places less centrally located and in case the kids'age.
I will try to give you other suggestions.