Expecting your driver to provide luggage assistance is a great idea, but be sure the driver understands he is expected to do this. I have had drivers who just sat behind the wheel of the car and made no effort to provide assistance.
They should use curbside check-in so the vehicle taking them to the airport can put their bags very near the appropriate check in counter. Generally the people who do curbside check-in will watch for people who need help and come out from the counter and help. There may be a small charge, and you need to tip these people, but it is almost always easier and less time consuming.
When we arrive at our destination there is almost always a porter who I hire to manage our luggage. If no one is available or my husband is being particularly stubborn, I get a cart and we put our suitcases on the cart and push it to the curb for our airport pick-up. I do not like to do this because lifting the bags from the carousel puts my husband at risk. Generally the person who pushes my wheelchair will stay with us long enough to retrieve our luggage.
When my own mother became difficult about accepting help, we had a serious discussion which begin with what I perceived as a selfish act on her part. When she refused assistance she dramatically increased the chances that she would injure herself. That would not only make her life more difficult but my life as well. So.....if she wanted to protect both of us she would use the wheelchair and luggage assistance. Once she got it out of her head that it was better to "bother" strangers than risk becoming an inconvenience for me she had a complete change of attitude.
We had conversations about several of her behaviors with this same logical argument. I remember that discussion and I do everything I possibly can do to prevent my situation from becoming worse, thus making me even more of a burden for my family.
Sometimes this sense of pride is applied in situations where it is just not appropriate, and sometimes you have to provide a perception check for your parents so they understand the risk they assume and the consequences of an injury to themselves, each other and ultimately anyone else who would have to provide care.