While I didn't copy all the details, the date I got from the wonderful book below is that Barent returned in 1697.This is on p. 202.I'm sure more details are in the book.
"Mohawk Frontier:The Dutch Community of Schenectady, New York, 1661-1710," by Thomas E. Burke, Fur, Cornell University Press, Ithaca and London.1991.
There is a great deal of information about the Vroomans of this period in this book, and it has a good index.However, it's a history, not a genealogy, and figuring out the relationships is sometimes difficult.
I recommend using the book along with Richard A. Hayes' website
Go to his homepage, which I'm pretty sure this is, click on the "families I'm related to," or something like that.Click on the Family Index, then V for Vrooman.In the index he gives whatever dates he has, so you can start with Adam or whoever early Vrooman you're interested in.Click on him and you'll see his wives, in order, his children, his parents.Click on notes for each, which gives his sources.There isn't a huge amount of detail.But you can find out who is related to whom, generations on end.He's a good researcher, and he updates his site every year or so when he gets new information or finds errors. I was looking at some Vroomans yesterday that he'd updated in 2010.
I recommend the book for everybody interested in early Dutch NY.It's the best I've read so far on the history of Schenectady, and it ranges far beyond that city to the general history of New Netherlands. Fascinating. I had to order it through InterLibrary Loan, and my library charged me $5.It was well worth it, and I'm going to order it again when I've entered more data from Richard's website into my genealogy program.Then more of the names will make sense to me.