As far as the issue with your mother-in-law, it's not that she can't come visit, she just doesn't want to. Some people are like that. Part of it is also a generational thing. My paternal grandmother never called any of us - she expected us to call her. As a result, she ended up home alone a lot.
As far as your daughter going there, does she want to go? Does she like traveling to new places and meeting new people? My older niece LOVED going new places, and hearing people with accents or speaking different languages. She came on a houseboat trip with my husband and I when she was 5 years old. We were out in the middle of a lake, so we had no cell phone service, but she never had a problem with homesickness. She was having too much fun jumping into the lake, being towed around on an inner tube, playing with the other kids, etc. Her younger sister never even wanted to spend the night at my mom's house until recently. She wanted to be at home with her mom. So I think a good portion of it depends on your daughter's personality. My niece flew alone at 5 (direct flight from Phoenix to LA) and spent a week with me without any problems. Can you try explaining to her what two weeks is, like "starting today, we're going to pretend that you're in Europe and you won't see Mommy again until two Saturdays from now." Every day tell her that she's only been gone for x number of days, and she won't see you again for x more.
As far as your MIL not having an internet connection, I wouldn't worry about that too much. My husband and I went to Italy on our honeymoon, and there were internet cafes all over the place. Your husband could easily find a place for an internet connection.
As far as the flight, if she likes to read, let her bring a ton of books to keep her occupied. What about a portable DVD player and her favorite movies ( and maybe an extra battery pack or two)? I'm not the greatest person technology wise, but if you have a portable DVD player and a video camera, could you make a DVD of you reading a story to her or just talking to her that she could take with her and play if she misses you? Maybe also have her pack her favorite picture of you and her.
You said that she's very excited about taking a trip with just daddy, so I think she'll be fine. I saw an interview with Gwyneth Paltrow once and she talked about how her Dad took her to Paris for the first time because "she should see Paris with a man who would always love her" or something to that effect, and I remembered it because I thought it was a really beautiful sentiment. If your daughter wants to go on this trip, at least she will be there with someone she's comfortable with. This trip will create a lifetime of memories for your daughter. It must be difficult for you to not be able to go; I know I'd want to be there for my daughter's first foreign excursion to see how she reacts to the new people, places, and food.
So if your daughter really wants to go, and you think she'd enjoy it, I'd let her go and tell her to have fun meeting her cousins, because who knows when she'll get to see them again?