akaymik85 wrote:The problem is, I don't speak Hungarian. My family spoke Slovakian, and are ethnic Slovaks.
Amendment of Act LV of 1993 on Hungarian Citizenship, i.e. the "simplified" procedure for Hungarian citizenship (http://www.allampolgarsag.gov.hu/images/angol.pdf):
– he or she or any of their ancestors was a Hungarian citizen or if he or she serves reason to believe his or her origin is from Hungary,
– he or she proves their knowledge of the Hungarian language
No way around the Hungarian language requirement if you apply via simplified naturalization.
akaymik85 wrote:I have two children, who would also technically qualify for simplified naturalization as they are my natural born children and therefore also descendants of Hungarians. Could my children (ages 7 and 5) apply for naturalization, and then I somehow become naturalized after my children do?
Only if your minor children have Hungarian citizenship today (i.e. inherited from their father) can you acquire citizenship from them (and then only if you live in Hungary for some years). Sorry, but unless your children acquired their Hungarian citizenship via your husband, who is now a Hungarian citizen, this will not work in your case.
Side note: I know zero about Slovakian nationality law, but if you are ethnically Slovak, have you looked into gaining Slovakian citizenship instead?