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 would fill gaps with polymeric sand, then lightly water the joint lines (think 'mist' not spray). The sand will 'set' like concrete, but with some flexibility, so it shouldn't freeze/frost heave.
Be sure to follow directions about packing joint and cleaning loose sand up before misting.
Best Answer
If the boards flex and bend under the load and crush the green concrete curb, you will be responsible for the full cost of the road crew returning to the site, removing the mess, and pouring new curbs.
Right now only the bossman thinks you're stupid. You don't want to hear the same thing from a judge.
If you can find some cement blocks or other firm braces, you can support the boards right next to the curb. Make sure it can't wobble. You're still taking a chance, though.
Don't do this job alone. You should have at least two helpers, one to watch the ramp as you drive onto it and stop you if it shifts or bends, and the other to hold your beer.