It's very nice of you helping your mom.
I guess your mom isn't a techy type. Maybe she has some songs that she wants to listen regularly. You can put them to her 3G from your computer/itunes.
You don't really need iTunes on regular basis. Maybe you can perform backup/add new songs and videos once in a while.
If you can't do the initial setup for her, she can bring the phone to Apple Store (hope she's got one nearby). As far as I can remember, swapping SIM cards and putting the iPhone under new person's account wouldn't require iTunes.
If she's got Wifi at home I think she can easily get by with $15 data plan.