As far as I know they could apply a visa together and she could put her 2 sons as dependant.And as well they could just pay one visa cost.Btw I remember iain asked the same problem I was having trouble finding the thread but here you go http://filipinaroses.com/showthread.php?t=8848 hope it helps!
mrs.daddy,
as long as they are under 18yrs old, they can go on their mothers app, and only pay one fee