I Heard it on the Grapevine

This is part of our grapevine that has escaped under the fence and into next door's tall yew tree........this tendril is growing out from the tree about 20 feet up.
I have grown to hate this vine because it is so prolific.......I chop it back several times a year ( hoping it will die) but it just seems to make it more vigorous :-/.........I find it intensely irritating that it grows so high and into the neighbours garden as it means I can't get to it to chop it off :-/
I would dearly love to have it removed as it takes up a prime spot on the only southish facing fence and all it does is grow out of control - it doesn't even produce grapes any more - but hubby won't hear of it, he says that it was here before I was ( which is true, he's my second husband) and it would be nearly impossible to dig out as its so established........so here it stays!
To be honest if we took it away next door's dilapidated old fence would probably come with it, so maybe it is better left alone .........and at least it provided me with a blip on a grey day :-)