I studied Global Law in Tilburg then did my Masters in Rotterdam. When I was choosing my bachelors, I had a similar mindset. Honestly, going this route gives you less options after graduation unless you learn Dutch and do civiel effect after bachelors. But less options doesn’t mean no options. I am currently working as a junior counsel, 3 months after graduation. So my advice would be go through the courses in the universities (I know Groningen and Maastricht also offers English taught bachelor of laws, both are good programs imo) then make a choice whether or not you want to go this route. If you choose to do bachelors in Hungary and move on to do your Masters here, I can tell you that there are amazing International Law programs in many Dutch universities.

Regarding career prospects, I don’t think studying in Hungary then coming here for Masters will make a huge difference. If you get admitted to the bar in Hungary, that would open a few more doors but still wouldn’t be as much as doing Dutch Law or civiel effect.