You need to find out if your cell phone will even work in Europe and what it will cost to use it there (can be quite expensive).

I doubt you will have much language barriers as you are going touristy places. These ships put in at the same ports all the time.

At sea, I would think you could wander off from your mother and her friends. There will be bars and other entertainment.

For an 11 day cruise, that doesn't seem like many stops. I would have suggested Florence for leather goods, but it doesn't appear Livorno port is on your itinerary.

Where are your hotels in Rome and Amsterdam?

I'm still looking for hotels in Amsterdam & Rome. I have more time during the day to search for bargains--Hot wire, Expedia.... My mom's ready to book hotels, once airline tickets are booked. I believe they are waiting for the air prices to drop out of JFK. Not sure if that's a good idea, but it's given me more time to research other accommodations not by airport. I'm very familiar with hotel in US.. But not out of the country

Livorno port, is that a great place to shop for leather? We have 4 days in Rome? Do you know whether renting a car would be economical? Or traveling by train will be easier?

A usual advice I give to first time travelers is to limit their selves on a small carry-on or hand luggage plus an average-sized luggage. No need for more suitcases than that, you will only make your life harder carrying more.
A tip that works miracles when packing is, see what you'd like to get with you, then try to fit in your piece of luggage. Lots will not fit. Prioritize and narrow down your choices and see what now fits in your luggage. Right. Now prioritize again and keep no more than 1/3 of the clothing. You are about good now lol
I am not familiar with cruise ships, but unless there is some etiquette on some areas, I do not think you need very posh/formal dresses on such trips. Focus is mostly sight-seen and go out for a few meals and drinks, some casual comfortable ware is fine unless you plan to attend the National Opera or something. It is very wise to have some comfortable walking shoes with you, I am impressed by how many people try to walk kms after kms on hills with ruins on flip-flops, definitely not a good idea. If your trip is of religious nature and you plan to visit monasteries and the like, it is important to have one top that covers your shoulders, a few places require women to wear long skirts rather than mini-skirts or trousers... Something that work wanders for such occasions is one nice pareo to wrap it around you and use it either to cover shoulders either as a long skirt while in monastery, and of course then you can easily use it to the beach too : ) Double-check if dress-code applies where you want to visit.
Even on October, sun is often shining in the Med, and even on a cloudy day, you can get sunburn, so do never and I mean NEVER forget to apply some suncream. One tube/bottle will hopefully suffice for your trip. My understanding is that suncream is much cheaper in US that in Greece and possibly Italy, so you may want to purchase one in advance.
Currency issues have been discussed very often in various Europe forums. In general most experienced travelers agree that using an ATM is the wiser thing to do rather than carry large sums of money with you, or use exchange offices. Nowadays traveler cheques are near extinction in Europe and not widely accepted-if at all-. You may want to use search box for currency issues, and have a look for pick-pocket issues too (wise to be informed on such matters, large groups of first time visitors are common target for petty crime).

How to pack for 17 days? You don't. Plan to have some laundry done in Rome before you board the ship, and then do it again in Amsterdam. Your hotel in Rome should be able to point you to a full-service laundromat within walking distance. I paid 7 euros per load (washed, dried and folded in 1.5 hour).

On Mariner of the Seas, laundry service is charged per piece, just like in a hotel. You may hand-wash small items and hang them in the shower stall overnight to dry, that's about it. (Pack a few light-weight hangers with you).

All the transactions on the ship, including booking shore excursions, are based on US dollars and are charged to your credit card. On shore, I used debit card to draw local currencies from bank ATM. If you have some local currency left over before leaving a none-Euro country, change those back into Euro at a money change place in the bazaar so that you may use the Euros in Amsterdam. (The money change place may not give you a very good exchange rate, but we are talking about a small amount of money here.)

I am sure you'll have a good time visiting all those exotic places.

Oh, I forgot to add that on sea days it will be a formal night. How dress-up you want to be is up to you and your group. If you don't feel like dressing up then you may opt to eat dinner at the buffet restaurant, Windjammer Cafe.