All she needs is a letter signed by her parents, right? Slovakia is only a 2 hour flight away. Something sounds odd.
Slovakia maybe only 2 hrs off, but there are no hourly flights, the DVO or SVO airports can be a few hours drive (in traffic) from Moscow, the event starts tomorrow, and to fix the documents is not simple....
No... it's more complicated than that. Plus Alina's situation (with official residence address and living not with her parents but under guardianship of grand-mother) makes her document more complicated in terms of precision of information.
It is not a letter. It is a form, which must be signed in person by both parents (if there are both parents) and must be notarized in person by both parents.
https://www.samso.ru/wp-content/uploads/2017/09/obrazec_soglasiya-3-litsa.jpg
Also, in some cases, if under 16 years old, there is a document for "temp. guardianship" for the coach or manager who is going with the child or a group.
The instructions are long...
http://zagrandok.ru/wp-content/uploads/2014/12/razreshenie-na-vyezd-632x600.jpg
http://zagrandok.ru/pomosh/razreshenie/razreshenie-na-vyezd-za-granicu-rebenka.html
https://xn--n1aiccj.xn--b1aew.xn--p1ai/folder/1146181
I don't know what Alina's document issue is..... but it is not a uncommon situation.
Alina's parents live in Izhevsk, that is their "legal place of residence". Alina lives in Moscow with Grand-mother, but her "official residence" is a confusing situation... actual address is in Moscow, but "formal address" is in Izhevsk, since she is a minor. Since Alina lives in Moscow, there is also a document of "guardian-ship" for the Grand-mother. All this "3-level" info has to be accurately and properly filled out in a form.
ANY mistake or typo, such as 1 letter or a number, in the form, which shows any variations in Alina's, Parents, Grand-mother's info (street address, passport number, date of birth, etc), will cause a problem at "border crossing station".
Just an example: if there is a number "230" and there is a mistake "280", it is a problem..
I see it happening often with my russian associates' teenage children travelling to language courses for the summer.
Unless the parents can either run to the notary public now, or fly to Moscow from Izhevsk, get it all done in 1 day, it is not possible to solve, and it seems like the event starts tomorrow.