Should the VP of the United States accompany the President on international trips?

Normally no. To risky that both could be taken out at once.
But, in the case of Biden and Harris - I think we can make an exception. In fact Pelosi and Schumer should go along too.

They have to be split up in case of an attack etc...

Not even feasible. Not even in the US. Too big a security risk. And why it doesn't happen in the US.

I think there is a general rule they are not out of the country at the same time