I am currently a master's student in computer science, doing research with one of my professors. They are a good mentor, and pay well. However, our research interests aren't quite aligned - they're related but I'm ultimately a little unsatisfied, and would like to pursue a PhD elsewhere. I also want to travel and potentially even move to Europe, so I plan on applying to PhD programs there.
So, I am thinking about applying for summer research internships at European universities. I think (and I need an unbiased second opinion on this) that a summer research internship could help me find a lab that I want to join for my PhD, as well as gain a second reference for future applications. Is this a good idea, given that I could otherwise spend the summer doing (funded) research with my existing professor?