JFK/LGA > AMS/CDG Airline/Airport Help.

Jet lag or travel fatigue can happen at any time and if you are able to sleep on the plane, may be very minimal.
Go non stop - less to go wrong along the way.
Amsterdam is easier for getting into town and timeliness. Walk down stairs, buy a ticket, board the train that runs every few minutes, arrive in middle of town in I recall about 20 minutes.
CDG is some distance. Either more expensive shuttles, or the locals trains which is not always great introduction to the city. You still have to get your way from the train station to somewhere else in town. Some find the Gare Nord to be a pickpocketer's nightmare.
All in all, Amsterdam is just smaller and kinder for a new arrival.

Having flown out of both JFK and LGA multiple times, I would MUCH MUCH rather fly our of JFK than LGA!! Also, not making a connection would be icing on the cake. If your family needs your help at at LGA, that would change the equation, though.

"Go non stop - less to go wrong along the way."
Absolutely. We find it less physically taxing than having to connect enroute as well.

Non-stop! Less grueling and no risk of missing your connection. I've never flown to Amsterdam but CDG is manageable. Early to mid-morning is a good arrival time.

Non stop JFK to AMS is the way to go; you have more risk of missing the connecting flight than your family getting lost going from NYC to the LGA assuming you all know English.

Another vote (as a New Yorker) for the nonstop from JFK. Those short Northeast hops like NYC-Boston are among the first flights to be canceled when there's bad weather or other problems.

Are you connecting in AMS/CDG or arriving to AMS/CDG? If you're connecting, AMS is a much better airport in my opinion than CDG. If Amsterdam or Paris is your final destination (in the sense of you will be leaving the airport from there), Amsterdam is also slightly easier to get out, but I think here I'd just defer to whatever your actual itinerary dictates is preferable.

You mention splitting off to your respective airports at the Roosevelt/Jackson Heights subway station. Be aware that there is no subway station at LGA so, from this station, you have to take a bus to LGA. The subway to JFK Is easy.

I vote for the flight out of JFK. Non-stop is always better. For a first-timer, AMS is easier to navigate than CDG. However, if you decide on CDG, this website is a great guide: https://easycdg.com/

If you are concerned about your family getting to LGA, I would recommend springing for a taxi or Uber or whatever to take them directly from wherever you are staying, rather than escorting them to LGA and ending up with a less ideal flight to Europe.

Put the family in a taxi to LGA and catch your train to JFK.

I'll do just about anything to not have a connecting flight including driving to farther away airports. While you are sitting around the airport (sometimes for a few hours) you would have been half way across the Atlantic by the time your second flight takes off. Send them in a taxi and take the direct flight- it's a no brainer for me.

UPDATE:

I'd be arriving at AMS or CDG.

Sept 5, 2021 it is open jaw trip unsure where I'm flying back home from probably somewhere south of the Alps Spain or Italy. I plan on spending 3-7 weeks in Europe. Roughly 3 weeks for Amsterdam-Paris-London--Gimmelwald-Munich-Berlin- Cinque Terre, Rome, Venice, Madrid Barcelona, Greece

I plan on spending 3-7 weeks in Europe. Roughly 3 weeks for
Amsterdam-Paris-London--Gimmelwald-Munich-Berlin- Cinque Terre, Rome,
Venice, Madrid Barcelona, Greece

Yikes! 12 destinations in 3 weeks, or just SOME of those 12 in 3 weeks?
There's sort of a big difference between 3 and 7 weeks! :O)

Let me clarify, roughly 3 weeks for Amsterdam,Paris,London,Gimmelwald, Munich and Berlin. I plan on revisiting Paris and London for Roland Garros and Wimbledon in the future but I HAVE to go to Paris and London on my first trip to Europe but probably won't spend more than 3/4 nights in each.

I do not know how much time I will spend in Cinque Terre, Rome, Venice, Madrid Barcelona, Greece or if I will visit all of the places in this secondary list. Wanted to go to Turkey but read a BBC article about people from the UK's red list were bypassing quarantine by staying in Turkey for 10 days.

Re: Timing arrival to manage jet-lag— I actullay prefer to take the early evening flights, landing in Europe at dawn. I book my hotel to "check-in" the night of the flight, so that I can get into the room early, take a nap and a shower, and be on the street again by lunchtime.

My first trip to Europe was to Amsterdam, great city. Been back once since then and still live it. I also would choose non-stop over a flight with stops any day. Also, I try to avoid flying into or out of LaGuardia whenever possible. I know they re-designed the airport recently but I still avoid it.

Let me clarify, roughly 3 weeks for Amsterdam,Paris,London,Gimmelwald,
Munich and Berlin. I plan on revisiting Paris and London for Roland
Garros and Wimbledon in the future but I HAVE to go to Paris and
London on my first trip to Europe but probably won't spend more than
3/4 nights in each.

In that case, I agree that you should take the direct flight to Paris, and spend the extra 20 to fly Air France. Then you could do an easy round trip by train across Europe. Paris-London-Amsterdam-Berlin-Munich-Gimmelwald is my suggestion (or the other way around if you prefer), after Gimmelwald you can take the train back to Paris to fly home, or book an open jaw ticket and fly home from Zürich. 6 destinations in three weeks is too rushed for me, but if it works for you then why not?