Your Dutch sounds like the 1920s because you learned it from an elderly relative whose language froze around the time her parents emigrated, and you have had little exposure to how Dutch has changed since. This is a normal heritage-language pattern, not a flaw in your ability. You can fix the mismatch with targeted exposure to modern Dutch while keeping the family connection.
Language changes constantly, and Dutch is no exception. Vocabulary, idioms, pronunciation, and even grammar shift generation by generation. Your grandmother was born in the 1940s to parents who left the Netherlands before her birth, so the Dutch she passed on likely reflects the speech of her parents and their generation, which can feel old-fashioned to Dutch people today. Words that were once common can sound archaic or formal, and certain constructions can sound stiff or theatrical. You may also be missing newer loanwords, slang, and everyday phrases that Dutch speakers now use constantly.
The good news is that this is very fixable. Start by increasing your input from contemporary sources. Watch Dutch television, stream Dutch YouTube channels, listen to Dutch podcasts, and follow Dutch social media accounts. Pay attention to words and phrases that repeat. When you hear something you would not say, note it and look it up. Use a modern Dutch dictionary or corpus to check whether a word is current, dated, or regional. Language exchange apps and online conversation groups can give you live feedback from native speakers who will naturally use present-day Dutch.
Be honest about the tradeoff. Your older Dutch is not wrong. It is a real variety with historical value, and it connects you to your family. You do not need to erase it. Think of it as adding a modern register on top of what you already have. In formal or written contexts, some older vocabulary may even be an asset. In casual conversation with peers, you will want to sound current.
Concrete next steps: pick one modern Dutch show and watch it with Dutch subtitles, note five new words per episode, and practice them in conversation. Find a language partner who is roughly your age and ask them to flag anything that sounds old-fashioned. Record yourself and compare your rhythm and word choice with a modern speaker. Over a few months, you will notice the gap closing. If you want structured help, a tutor who teaches contemporary Dutch can speed this up, and resources like Dutch Fluency may offer relevant guidance. Most importantly, do not be embarrassed. You learned a living language from a loved one, and now you are simply updating it.