For the next 2.5 months you need to take what you get. Any seed planted now, especially adjacent to a driveway, will die. Tender new roots cannot survive a normal summer heat. This means you will have some weeds come in to fill up the bare spots. Just tolerate those weeds until fall when you can take care of them and reseed.

Hard soil is not a good reason to add topsoil; however, low spots are a good reason for topsoil. Sounds like you're doing that okay. If you do add topsoil, use your feet to stamp it down before you put the seed on. Stamping it down will reveal where the low spots are going to be and you can add more topsoil right then and there. Stamp that down, too, to make sure you have enough soil. Then apply your seed on top of that...and stamp down the seed. That is all you need to do when starting with new topsoil.

As you probably know from your quotes around your mom's comment, you don't need to mix up the soil to aerate it. Mother Nature does not have animals roaming around mixing up the soil to aerate it. She has animals going around stomping on the soil and pressing seed down into the surface.

Your seed mix might have had some Kentucky bluegrass in it. Check the Guaranteed Analysis printed on the side of the bag. Kentucky bluegrass takes 3 weeks to sprout once in the ground and kept moist. There is a slim chance that some of that has germinated and a further slim chance that some of it will survive the summer. Kentucky bluegrass is the type of grass which spreads to fill in bare spots. The other type of grass in your mix is likely a type of fescue. Fescue is a "bunch grass" which grows in tight little clumps. It can spread but only by enlarging itself. If you want to have a dense coverage, you either need lots of fescue seeds or 10% or so of Kentucky bluegrass seeds. One secret you need to know is that fescue seed sprouts in 2 weeks while the KBG takes a week longer. What often happens is people will see the new grass coming in and back off on the daily watering. This leaves the KBG at a stage where it was almost ready to sprout and then it dries out. KBG requires full sun, so if this spot is under a tree or between buildings/fences, then the fescue would be your only choice of seed in your area.

Here are the basics of lawn care for mature grass. You can practice these principles on the rest of your lawn. For now your new seeds need water more frequently because of the shallow roots and new growth.

2. Water deeply and infrequently. Deeply means at least an hour in every zone, all at once. Infrequently means monthly during the cool months and no more than weekly during the hottest part of summer. If your grass looks dry before the month/week is up, water longer next time. Deep watering grows deep, drought resistant roots. Infrequent watering allows the top layer of soil to dry completely which kills off many shallow rooted weeds.

3. Mulch mow at the highest setting on your mower. Most grasses are the most dense when mowed tall. Bermuda, centipede, and bent grasses are the most dense when mowed at the lowest setting on your mower. Dense grass shades out weeds and uses less water when tall. Dense grass feeds the deep roots you're developing in 1 above.

4. Fertilize regularly. I fertilize 4 times per year using organic fertilizer. Which fertilizer you use is much less important than numbers 1 and 2 above.