I have a huge stand of scrub oak right next to my paver patio, and surrounding an enormous pine tree. It seems obvious that I must use an herbicide and kill the oak. If I am very careful not to get it on the pine tree, am I endangering the pine anyway when the herbicide goes into the roots of the oak, which might be in proximity to the pine roots?

YEP !!! Cut them down low, and keep spraying, new growth, with 5% white vinegar. It will take a while for roots to, finally die, butt, they eventually will.
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Cut down the oak as close to the ground as possible. Grind the stump out. They will not grow from roots so you would only need to grind it to just below soil level.

Otherwise, CAREFULLY paint the oak stump (top and sides) with full strength brush killer. Don't get any on the ground as it will kill the pine. Oaks are tenacious; it may be a year before the oak gets over the brush killer and grows again.

Why does it seem obvious to use poison?
At my house, cutting the tree down, and cutting the sprouts off with an axe after they get large enough to bother with is generally enough.
If necessary, cut any returns.
The secret is to let the tree stump get invested enough in the new sprouts, that cutting them once exhausts the roots.
I can put in vegetables after this action. Matter of fact, I am putting in vegetables in what was a grove of trees last year at this time. No grinding, no poisons, nothing to it.

You can cut down the scrub oak and be vigilant in hacking away any new suckers that appear. No poison/herbicide needs.

Or, read this article. You can use a very small amount of herbicide to kill the trees. Once they are dead, cut them down and you should have no more re-growth.
https://garden.org/ideas/view/...

I don't see, in the original post, any mention of an oak stump - just the little sprouts. I think they can be safely treated with a wipe-on herbicide. Mowing/cutting them close will not necessarily ever discourage them; I have a similar sounding stand of little oaks that I have been mowing like lawn for over ten years - and they look a lot like rather strange lawn, very much alive.

If they're just sprouts.... I use a mattock.
... Generally not much regrowth from that...
Stupid electric company came on my property and sprayed poison on my trees.
Looked horrible, and... Dead wood is a lot harder than green.
Made it very difficult to clean up.
Real easy when trees are alive. Next to impossible when trees are dead. Still have some dead trees standing that I can't cut out with hand tools.

Laurie : If you use a systemic herbicide ! It will interact with intertwining roots, of desirable tree, or plants.
Vinegar, is just a contact killer. It won't hurt anything you don't get it on. Just use a peice of cardboard to protect your tree.
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