Toxic in what regards? If it kills weeds, then it does have some toxicity. Unless it is horticultural strength (20% or more), vinegar is a very ineffective herbicide and generally requires several repeat applications and even then will not kill off brush or any perennial weeds. And if it IS of horticultural strength, it is quite toxic/caustic, requiring protective clothing and goggles. Note: vinegar is not approved as a pesticide under law so application directions may well be lacking.

Your least toxic method may be to mow the weeds/brush as short as possible and either till into the ground and cover with a layer of wood chips or just smother the remains with the chips.

Most intelligent people would think twice about using a glyphosate herbicide on two acres of weeds. Spot treatments are reasonable, but only if the user is capable of or willing to read and follow the directions carefully.

Rachel, have you contacted your local extension service office to see if there is an expert on hand who might be able to help? Someone with weed management expertise in farm fields will be able to help you with some environmentally sound ideas.

There are commercial herbicides formulated with vinegar (horticultural grade) but I don't think that it's a good option. Not only is it a hazardous substance, but it's simply not effective for most weeds.

Round-Up is glyphosote,and is cancerogenous.

I hate to tell you but that is an unproven allegation .... not a fact. It is driven by lawyers, not scientists.

If you mow it on a regular basis, aerate, overseed and lime and fertilize as necessary, it will eventually look pretty good.