I think you are unnecessarily worried, Matilda. Your son will probably grow up speaking mainly English. However, if he is lucky, he will also speak and understand Dutch. Babies seem to be able to process more than one language with little or no difficulty. In fact, if you want a child to be able to speak another language, the time to begin exposing him to it is during infancy. It is done in Europe all the time. Children there often become fluent in three or four languages.
To relieve your anxiety, you might want to urge his grandparents to use primarily English when they talk to him. But do it gently, and take the blame on yourself (“I’m not lucky enough to understand and speak Dutch”). It sounds as though they are providing wonderful childcare and you don’t want to jeopardize that.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.