Hmm, OK, I will consider that. I was trying to make this border with my neighbor look better sooner rather than later, as their lawn looks gorgeous and it's a bit of a dump on my side. Hoeing that clay is not a pleasant prospect when it's hot and dry in August and September. It will be like rock. In the event I have to use some herbicide, what do you think about the question of how long to wait after that before planting seed?

It looks like you have Sedge grass coming back Ortho backs a product just for sedge as for the Round up it way not be sticking to the leaves/blades on it they make a product to add to it so it adheres to waxy type plants . It might also be Bermuda grass check to see if it has rhizome type roots if so it will take several applications of round to kill it and I wouldn't mix it to strong or it might keep your new grass from doing well . Sedge is a paler or yellow green than Fescue or Kentucky Blue

I have used Roundup around the base of many trees and it has never harmed the trees. I would never (again) use a weed barrier like plastic. I believe the rule-of-thumb for mulching around trees is no more than 6" deep around the tree.

Before getting to organic weed killers, everything else you want to do will lead to disaster. Tilling is very wrong and seeding in the spring is very wrong. Currently your soil has a capillary structure built by living and dead roots, worms, beneficial insects, and by microbes living in the soil. When you rototill you destroy that capillary structure and turn everything into fluff. Over the next three years that fluff will settle back into a new capillary structure. When it does it will settle unevenly due to the way rototillers jump around in the soil. They hit a root or rock and buck up out of the ground leaving a spot un tilled. Or they hit a soft spot and dig in deeper than the rest of the area. These underground hills and holes eventually result in surface hills and holes as the soil settles in. The settling starts immediately and continues to worsen for about 3 years. The best thing you can do is work at the surface by scraping down any high spots and filling in the low spots with that soil or with new sand. If this turns into leveling the entire yard, it is still not that difficult for a homeowner to do. You need one tool you probably don't have, a drag. Let us know if you want more details about that or search this forum for topics about leveling. Seeding in the spring is a problem for two reasons. One is that NOW is the time crabgrass seed wants to germinate. If you put down new grass seed, the first grass to come up will be crabgrass. Crabgrass is a summer annual weed that features rapid germination and establishment as well as excellent adaptation to the heat and drought of summer. As you continue to water the new seed, the crabgrass really gets a head start. The grass you seeded, fescue, rye, and/or Kentucky bluegrass, is not adapted to rapid establishment in the warm season nor will the tender new grass plants tolerate the summer heat. What you will have by July is a yard full of dead fescue and overtaken by a blanket of creeping crabgrass. So now what? What I would suggest is to nurture your weeds this season and in early August, start the process toward renovating the lawn. Start by killing the weeds and surfacing the soil. This can be done in one step if you hire someone to run a tractor and box blade over the surface. For a residence that takes an hour or so assuming he has access to the yard (no fence or wide gate). Then seed, roll the seed down, and start watering. By waiting you will avoid the crabgrass problem and give the grass a great start. It will develop roots all of fall, winter, and spring making for a great lawn by the next summer heat. As for organic weed killers, the only one that works is vinegar on a hot day. And that only kills the surface of the plant. The roots typically survive the treatment as do weed seeds. If you reapply often enough the roots will eventually die from lack of photosynthetic nutrition. The best vinegar to use is 20% vinegar which is only used in agriculture. You have to be very careful with that strength of product. Household vinegar is 5% acidity. The 20% will cause blindness for months if you get the spray in your eyes. It also causes immediate respiratory distress if you inhale it. Also some weeds seem to be impervious to vinegar while others shrivel up in 20 minutes. I have used only organic fertilizers since 2002 and sincerely believe in the benefits; however, I have used RoundUp painted on certain plants/trees to kill them when needed. I am not a RU fan, but if you need it you need it. There are other herbicides that might be plenty strong for your purposes. I would avoid using them until August, though, if you want to keep a green looking "lawn" for this growing season. You might post a picture or two here to see how salvageable your yard is. You might be able to have a fairly nice lawn by May if the cards are all right. Do you remember what kind of grass you have? It's going to be fescue, rye, and/or Kentucky bluegrass.