Contact your local town, and ask them if it is acceptable for you to add some asphalt mix to make a small ramp there, adequate for a wheelchair to roll up. Make sure they understand why you want to do so, that it is necessary for wheelchair accessibility for your father in-law. Then follow their directions. You might even be surprised and find they do it for you if you asked nicely.
Edit: Another possibility - find a contractor who can grind down the curb in one part of the driveway. While this too may require permission, it may be easier to obtain, since no mods would be done to the road surface itself. If you are handy, you could probably do the work yourself, with a small (rental) electric jackhammer.
My approach would be cheaper yet. Cut many parallel kerfs in the curb with a diamond blade in a Skilsaw or an angle grinder. You can buy such a blade for only a few dollars at your local home center. Make these kerfs no more than about 1/2 inch apart, and slope the depth of the kerf so that the cuts are deepest at the street. Now, take a hammer and cold chisel, or an air powered chisel, and break out the material between the kerfs. Done carefully, this will leave you with a nicely sloped curb that a wheelchair can ride up over, and nothing on the road itself to upset the town. You can surely do this in a way that looks as if it were professionally done if you take your time.
Of course, if you do this work yourself, use ear protection for the noise and definitely wear a respirator. That dust is terribly bad for your lungs.
You have divots in a concrete driveway.
I'd saw around the divot area, break it all out, and pour concrete, rather than anything to do with asphalt. Drill some holes in the edges and insert steel to tie the patch to the slab.
If following the "quick fix" fill-on-top approach, possibly thinset (tile cement) but trying to do anything with concrete in the winter is fraught with difficulty - you have to heat it up and keep it warm - if it freezes before it cures, it's toast.
My gut says that your quick fix with hot tar is going to be good for 6 months, at most. Additionally, it will complicate doing a good concrete repair later.
Best Answer
There are 2 types of concrete: Concrete that that is cracked and concrete that will crack.
There are several products that work well to seal cracks. Oover the years I have found the types that stay flexible to be the best —especially if in a region that has low winter temps below 25F. Below that temperature, I find water will cause more damage if not sealed.