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Yes there is a theatre. There are 2 performances of the show each night. they have to cater for 5 languages, so no stand up comics. They tend to be a mixture of music and dances; other visual acts like Cirqu du soleil style and classical music performances.
they do have a children's programme. If you vist the forum for MSC on cruisecritic.co.uk, the person incharge of the kids programme has a thread going in which he describes all the activities and answers questions from posters. It seems from some of the posts that the kids really like him and his team as there are many thanking him after their cruise. If you are considering a caribbean cruise, then a lot of the children will be North American, however if in Europe then there may not be so many english speaking children. However they do cater for English.
Have travelled on Musica (sister to Lirica) - I strongly suggest you read the reviews on this site regarding MSC. You dont say how old your grand daughter is, but my 11 yr old did not like the look of the kids club as it appeared very 'babyish'. Reports from other parents were that they quickly removed their kids from the club as it was not well supervised. English are very much in the minority. The theatre provides approx 1/2 hr shows of mime/acrobatic type acts so that they dont have to translate into five different languages. In the day you can get the usual burgers, chips, pizza for the kids. In the evening on the main Dining menu you can have as an always available: Chicken Breast, Thin Beef Steak and Spag. Bol. but be warned the buffet closes at around 6pm and converts into a chargable Bistro. There are no alternative dining options for the kids, eat in the main dining room and thats it. Pay for water, tea and coffee.
I suggest that you go to the cruise review section on the left select MSC line loads of information there be warned it is not very encouraging reading , you may want to consider another line maybe RCI or P&O best of luck & enjoy your cruise.