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.
I'll let others chime in with gutter ideas. Just keep in mind that you'll need to make sure they can handle the expansion from ice without cracking. But I did want to mention a few alternative solutions you may want to consider.
If you want to keep the lawn, you may consider at a french drain, possibly with some ground level openings to handle severe weather (install these in a way that you can close them in the winter).
If you want to change the look, consider some raised beds on either side of the driveway (which has an added benefit of keeping cars off of the lawn).
Best Answer
A very common dust control agent for road is Calcium Chloride it uses hygroscopic properties that allows it to retain water molecules. It hydrates and forms a "liquid layer" that helps dust particles to stick and hold, this on the a road suppresses formation of dust.
The dirt roads in front of our home and surrounding streets are sprayed annually by the county maintenance to form a hard dust free road.
As and alternative a coating like Soilworks Gorilla Snot which is a biodegradable liquid copolymer that is sprayed on for erosion and dust control.
For the last 8 years the near by Marine Air Station has applied it for dust and erosion control on the training range.
As of this last summer it was started being used by the state highway department on desert areas near Tuscon/Phoenix to keep dust storms from causing traffic wrecks on the near by freeway.