I'm trying to book a flight for my mom to Shanghai by using my AA miles but I'm not sure if I should use Anytime Miles or MileSAver Miles. If I booked her Anytime miles would the possibility of getting her upgraded to business class be higher? She will be traveling with my son who is not yet two so he will be sitting with her. I just want to make sure she's as comfortable as possible on this flight. Please advise. I've only used my miles once to book a flight for my mother in law to fly from Florida to Ohio and she didn't have any issues. In fact, she said they put her up front in the business class and gave her a glass of wine. Thanks for any suggestions.
Upgrades on long hauls are usually only offered when economy is oversold and there are no re-routing options for passengers they have to bump. They are not common and the chances of your mother reaching the top of an upgrade que is next to zero.
When choosing who gets upgraded, elite frequent flyers get the highest priority, ordered by their elite level and the ticket they are flying on, followed by full fare paying non-elite passengers and then down through the fares from there.
While having a FF ticket paid for at AAnytime levels puts her ahead of a person holding a ticket paid for at MileSAAver levels, that distinction likely would not come into play.
You don't really specify it, but it sounds like you plan for your son to travel as a lap child. Going from the states to Shanghai is a long time for a child almost two to sit in a lap in an economy seat. Your mom is a saint to volunteer. Have you looked at using MileSAAvers to get her a business class seat from the get go?