There are no trains now neighter from Vilnius nor from Riga to Ufa.
The closest places where trans to Ufa can be cought - Minsk and Moscow. There are many trains daily to Ufa from Moscow and 2 trains per week - from Minsk.
Travel through Minsk will be slightly cheaper, but trains from Minsk to Ufa are slower.
Also you should take into account whether your mother need Byelorussian visa (you didn't told what nationality (citizenship) she has).
Есть поезд Калинингад-Челябинск который идёт через Вильню и Уфу. Но он курсирует нерегулярно (по числам).
[/qoute]фиг там, нету его даже по числам.