Return Taxi and Carousels

How about the model boats in Luxembourg gardens. Lots of space to burn off energy and play with other kids....though 3 is pretty young for the boats.

Your hotel is staffed by incompetents. There is no problem getting a taxi for as many as 7 at the airport queues. You may wait a little bit for one to be brought up but van cabs that seat 7 passengers are very available. You can also order a cab from g7 taxi the night before a return trip to the airport (or train station) and specify the need for one that takes 6 people. There is a 7 Euro booking charge ahead but well worth it for the airport. It would be 50 or 55 depending on which side of the river you are on for taxi to or from CDG plus 8 Euro for the two passengers above 4 -- 4 Euro additional each on any taxi ride. Are you staying near the airport for several days to visit Paris? If so, bad idea and expensive commute. The fixed fare is from the airport -- I don't know about hotels in Roissy. If your hotel is AT the airport then use the airport queues for the rate.

The Tuilleries and Luxembourg Gardens have many toys for children but neither had carrousels last time I was there. There is one in the Tuilleries at the end of summer in a little carnival would think that would be gone by now. But there are lots of small carrousels in Paris -- there is an endangered species carrousel at the Jardin Plantes, an antique carrousel that is totally adorable in Square Batingnolles (but of course off season it may only be running late in the day for after school if at all). They are here and there on traffic islands -- saw one near Villiers metro and near St. Paul metro. There is one in Parc Monceau. And a couple near the Eiffel Tower. There are little pocket playgrounds here and there around town with bouncy horses and such for littles. There are nice playgrounds in all the big parks including the Tuilleries. And often late in the day there are rental toy sailboats there for the fountain pool which kids love. If you are there for several days the Jardin Acclimatation would be lovely for an afternoon with the child -- but not practical for a quick day in Paris, so you will have to keep eyes peeled for carrousels as you move about:
https://janettravels.wordpress.com/2019/09/18/delights-of-jardin-acclimatation-and-fondation-louis-vuitton/

I find your post very confusing. Are you arriving at Gare du Nord and then heading to a hotel at the airport. If so why would the hotel in that context be commenting on the presence or absence of large taxis at the airport? Shouldn't they be commenting on the presence of them at Gare du Nord? Are you going to Orly or CDG from Gare du Nord? From your post, I think you are traveling from Gare du Nord to an airport (BTW, bad idea if you are planning to stay in a hotel at an airport for a trip to Paris but that is covered in detail in the first response). I just can't figure out from your post which airport it is that you are going to. I have flown into and out of both. The longest that I have to wait for a large taxi at CDG was about 10, maybe it was 15, minutes. In contrast, the last three times that I flew into Orly, our group of five had to split up because after waiting 15 minutes, there still were no minivan taxis available. That being said, the times that we were six in a taxi from CDG, we only fit comfortably in the taxi because four of the six were either petite women or children and we did not have a lot of luggage. So, I would not say the hotel is staffed by incompetents until I know more about which if any airport you are looking at for a maxi taxi, how much luggage you have, and how large the people, other than the 3-year-old, are in your group.

Sorry to be confusing. We arrive at CDG and stay in 2nd arrondissement for 3 days then we need to get back to CDG to take a flight to another part of Europe. We have to come back to Paris to end our trip which is why we come back through London at gare du nord and are staying at a hotel by the airport for the finale of our European tour. So I am glad we can get a cab at the queue for 6, and make it to our hotel. Then when we go back we can book it from that website and then from the train station catch one a last time. We have 5 adults (2 slender 3 not and 1 toddler in a car seat) we have carry on luggage only 8 bags in total.

The car seat might be a deal-breaker for fitting six into a large size taxi. Maybe have a plan B of splitting into two groups if needed but try for a large taxi. It's a 45-minute drive from CDG into Paris and IMO comfort is king. I am probably more sensitive to this than most because I am a 6' woman married to a 6' 4" man with 2 children who are over 6' tall as well as having an extended family very tall people (and athletic, think former NFL linebacker, volleyball players and a track star are some of my family members who sometimes travel with me) and just because 6 of us can fit in a taxi does not mean that we do it.