You learned Dutch from a heritage speaker whose language froze around the time her parents emigrated, so your vocabulary, pronunciation, and grammar reflect an older version of the language. This is not a flaw in your Dutch, but it does explain why modern Dutch speakers hear it as dated. The good news is that you can update it with focused exposure to current Dutch without losing the family connection.
Why this happens: languages change. Words fall out of use, new words appear, and pronunciation shifts. When a family leaves a language community, their speech often preserves features that later disappear or change in the home country. Your grandmother was born in the 1940s, but she learned Dutch from parents who left earlier. That means some of her Dutch may already have been conservative, and it stayed that way because she had limited contact with later Dutch. To you it sounds normal because it is the only Dutch you have known. To people in the Netherlands, it sounds like a time capsule.
What to do:
Listen to modern Dutch daily. Podcasts, news broadcasts, YouTube channels, and Dutch TV shows give you current pronunciation and slang. Aim for at least 20 to 30 minutes a day.
Read contemporary Dutch. News sites, blogs, and social media posts show how people actually write and speak now. Notice words and phrases you do not recognize.
Track the differences. When you hear a modern word for something you say differently, write both down. Over time you will build a personal list of outdated versus current terms.
Speak with Dutch speakers who are not family. Conversation groups, language exchanges, or online tutors can give you honest feedback. Ask them to flag anything that sounds old-fashioned.
Keep the family Dutch. There is no need to erase it. Code-switching between your heritage style and standard modern Dutch is a skill, not a problem. Use the old forms with family and the new ones in daily life.
Honest tradeoff: you may feel self-conscious at first, and some people may still find your accent charming or unusual. That is fine. The goal is not to sound like a broadcaster but to be understood and to feel confident. If you want a structured way to measure progress, a program like Dutch Fluency can help, but daily exposure matters more than any single course.
Next steps: pick one modern Dutch podcast and one news site, use them for two weeks, and note every word or phrase that differs from what you say. Then practice those with a language partner. Your Dutch will not become 2020s overnight, but it will move in that direction faster than you expect.