hey hey addiez237
welcome to the forum
my own opinion is you are planning tooooooo much in your short days. where are you flying in from (USA, Canada, european country?) what time do you arrive on the 16th? that really is a "lost" day, land with how many other planes, getting through immigration/passport/getting baggage, getting to a taxi ( E56 or E65) to take you to hotel or private ride? make sure they take credit cards, if not wait for one that does or have cash euros), accept 4 people and luggage (pack light), where's your hotel? check-in times 3-4pm check-out times 10-11am, first day is jet lag which may just be a roam around/relax day.
not knowing what attractions/activities you're planning to see and do, make sure you have reserved them direct from website. you are traveling during high high summer season, HOT, with crowds everywhere. be prepared. make reservations for restaurants, many close during afternoon hours and open 7pm and later.
i would drop chamonix, it's outta the way that takes so much travel time that you really don't have or want with more time either driving or trains. several years ago we were in hotel near gare de lyon train station, walked to station got snacks and boarded for our trip to annecy. from station hotel to annecy hotel taxi to our apt was about 5 hours. guessing to chamonix would be another 2 hours. do that on another trip.
trains are city center to city center, so easy. having a car is a PITA, trying to follow maps, parking is slim to none, lots are further away than you think/want, do you need an IDP for each driver in a different country (internationaltravelpermits.com) (aaa.com/IDP).
read about rules /laws about driving, parking, ZTL's (no driving in city centers), how big a car for you 4 and luggage, insurance. some rentals shops may not ask but if stopped for any reason the popo may ask, be safe than sorry if they give you a ticket to pay right on the spot. lots of changes with travel in europe nowdays with thousands & thousands traveling the same places you're planning. doesn't seem to be a low season anymore, many big cities are busy all year long.
take train to provence and rent car down there. pay attention to hours car rentals are open, some 1/2 day saturdays and closed sundays.
been about 4-5 times to paris, BFF is french basque and her favorite city is paris. been to many places around the city, we both have some mobility issues and have just grabbrd a cab which was good for us. found out of the way restaurants instead of many popular ones mentioned here. my go to was to eat crepes and souffles (lesouffle.fr, le recaimer, la cuisine de philippe) plus on a mission for french onion soup and eclairs. it was a fun time
o-chateau.com
did wine tasting, champagne cruise on the seine (private lounge at front of boat, tasting 3 champagnes with an "oh la la" sommelier
cruising down the seine to see the attractions along the way.
drop car off in provence and take train to nice so no hassles/stress. your last day, may 29, is morning duties, breakfast, check out get to train/airport for flight home. enjoy the few days you have in nice to roam, have fun. another hint we did was grab some food/meal for flight back. hope this gives you some ideas, have your kids help with research. we did couple columns: must sees, ok if time, no time. keep track of days/times places open. good luck
aloha