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).
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I would put the drain as close as is possible to the door jamb. Think about driven rain hitting the door and dripping down it. Where do you want that water to go, into the drain or back under the door?