One aditional factor you may need to investigate - with no APs could she even get admitted? The Slovak school system and final maturita exam is accepted by UK universities as equivalent to A levels, whereas they want APs for Americans.
This college in Bratislava which offers an American style liberal arts degree for 4K (in euros) says they assess academic ability of non-EU applicants on “the results of secondary education and the results of the leaving exams.” (Even if your daughter is a Slovak citizen, her education is not in the Slovak citizen so I’m sure she would be assessed as as an international.)
http://www.bisla.sk/criteria-for-admission-for-2017/2018
Costwise, it looks as if they definitely charge fees for courses taught in English (up to 12K euros, although my guess is that higher price would be for something like engineering). This link may be useful: https://www.saia.sk/_user/documents/publikacie/study-in-slovakia_2015_web.pdf