Espe,
As the others have indicated, it's not recommended to buy advance train tickets to connect with an inbound flight. Some of the trains you'll be using will have compulsory seat reservations which are specific to train, date and departure time, so can ONLY be used on the one train listed on the ticket. If you miss that train for any reason, your tickets are worthless and you'll have to buy more.
While you could leave a cushion of several hours between flight arrival and train departure, that may mean sitting around a train station in a jet-lagged state which is often a miserable experience, especially if you see trains departing that you could have been on if you had bought tickets on arrival. Add to that the miserable experience of being stuck on a train in a jet-lagged state for 8 hours or more to reach your destination. Keep in mind that the train from MXP to Milano Centrale takes about an hour, so that has to be included as well.
I wouldn't suggest using Rome2Rio for definitive information on train schedules. It's good for a general idea, but I wouldn't rely on it for specific information. I have no information on Loco2. Your best source for rail schedules is Bahn.de (German Rail website) but you won't be able to buy tickets there for Italy and France. A good place to buy tickets for both Italy and France is www.captaintrain.com.
While you can save money with advance purchase tickets, as mentioned above that's not the best idea when connecting with a flight. The ticket prices likely won't increase, as the schedules won't be updated until mid-June.
Here's a summary of the tickets you'll need.....
- Malpensa to Milano Centrale - buy tickets at the airport rail station. Note that you MUST validate all tickets prior to boarding the train or you'll risk hefty fines, which will be collected on the spot! Also, the Malpensa Express has two routes, one to Milano Centrale and one to Milano Cadorna, so BE SURE to board the correct train! You'll arrive on Binario (track) 1 or 2 at Milano Centrale, and will then have to make your way into the main hall to find your next train.
- Milan to Nice Ville - it's possible that you may be able to connect with the 11:10 Thello departure, and you should be able to buy your ticket at the MXP rail station for the segment from Milan to Nice. The tickets will include the seat reservations.
- Nice Ville to Marseille-St.-Charles - as this is a TER (Regional) train, it won't have any seat reservations so I might try to buy advance tickets in this case (use Captain Train for that). You will likely have to validate them in the composter un billet machine before boarding the train (hopefully someone else can confirm that).
The trip described above is one of the shortest trips from Milan to Marseilles at 8H:20M. The Trenitalia website currently shows tickets on the Milan-Nice segment at €45 PP for adults and €22.50 PP for children (but I don't know what ages apply to the child fares). I didn't check prices on the Nice-Marseilles segment.
While I can appreciate the desire to save money for a group of four, I suspect this will be a dreadful and tiring travel day for all of you.
Good luck!