We inherited two vines when we moved into our new house - one a red grape and the other white. They grow either sider of a big arch and meet in the middle. OH cits them back every year but in the growing season they are rampant. Throughout the year he cuts back the bushy bits not bearing grapes. After all the rain we've had they have exploded again, like a mad frizzy perm, all over the arch.
I think persistence is the key. OH started off by being careful where he cut them back - now he just goes for it to keep them slightly contained. E get lots and lots of grapes and this year we have decided to do something with them other than enjoy the odd few picked from a bunch when we are out in the garden. The birds love them too and when the grapes fall, the mess on the flag stones below is horrendous. If we don't get our act together and try making a few bottles of wine this year, we have decided we will cut down the many, many bunches of grapes and put them in big bowls and let the grandchildren trample them in their bare feet. Very rustic and maybe a learning/play experience?
Sorry I cannot give more advice, but I understand the problem. They seem to put on a yards growth overnight in this weather!