Did you think about maybe getting on the internet and using Instant Messenger to contact the family? I have done that in the past and it worked very well for us.
You may or may not have cell phone service while at sea. And depending upon where we are, you may be making international calling. I would give Verizon a call. When I had my Verizon phone, I lost service as we pulled out shortly after sailaway. I did have service while in the Bahamas, but don't recall if I ever did call home from there - don't think I did since I was IM'ing them anyway.
In some magical land far, far away, I don't care if the phone don't work for four days!!!

OK,OK, stop laughing at me. But in reality with parents who have health issues, ours are always on. We activated our phones for international use, in case of a crisis at home. If you are leaving people home, you might want to call your carrier to see what the rates are and ask if you have do something special to your service because you are leaving the United States. This can usually be done just for the month you are gone.
We call home as we pull away from the pier for a final worrywart check of both parents, and then hang up.
The rules to call us from Mon.-Wed. are as follows: death, blood shead, major surgury. It's not that we don't love the family and friends, but we are running away from you for a vacation. I think they can last 3 1/2 days without constant contact. We value (and pay a lot) for our private time here on the ship and the island; it's the only time we really get to spend with each other, and that is sacred to us.
Otherwise most people know we are away and don't call until we get home. WE call the parents everyday, just to check up on them and ease our minds.
I don't know how the IMing works, since we don't do that