You are working against how Apple designed the system to work. You should be changing your account's country settings to Hungary when you reside there, not create a second account. Using two accounts can create multiple problems and it isn't a solution to wanting to download an app from another country. The system isn't designed for people to have access to more than one country's store. Apps and media have regional licenses and you are only supposed to use the store country where you reside. I know people find this unfair but it is the way the world works. I too have moved country in the past and I just had to say goodbye to some old things I liked and embrace some new ones.
The support article Change your Apple ID country or region - Apple Support describes how to change your country setting on everything using your Apple ID, and the requirements and results of doing this.
Changing store country is not a trivial endeavor. The system is set up to only facilitate doing this if you are moving to the other country to take up residency. It makes it difficult for people to temporarily change country settings to do things such as get around distribution restrictions only allowing them to buy items available in the country where they live.
"Redownload your apps, music, movies, TV shows, and books on any devices that you might use to play or read them in the future. Some types of content might not be available in your new country or region. (Learn what types of content and services are available in your new country or region. - Availability of Apple Media Services - Apple Support )"
Oh, that "at this time" message Apple doesn't like something about your data entry. It may be something is inconsistent with the information you are trying to enter and the country for which you are entering it. It doesn't say what. It may be you are trying to use a Korean credit card billed to you in Korea. It may be you need one billed to you in Hungary.