Sight seeing questions in Paris

I'm not one to do museums on arrival day, but what makes the Rodin so magical is the outside sculptures and gardens. So you'll be strolling and getting fresh air. But, L'Orangerie , also wonderful, is a small manageable museum and in the Tuilleries so you can stroll in gardens after. But sounds like L'Orangerie is closed on Tuesdays.

I think you would need to reach out to each museum (or check the website) for any allowable luggage sizes in the cloak room. I wouldn't be concerned about it being secure. They are more worried about what you are trying to bring in; (everyone goes through security) not trying to steal from you.

Also, you can use the G7 official Paris taxi app to get a taxi to Gare St Lazare for time effienciency.
We arrived closer to closing time at the Rodin this past spring. So we only saw the outside sculptures and gardens; we never saw inside and we really enjoyed it! So since your time is tight, you may want to do the same thing.

The Musee Rodin opens at 10 AM and L'Orangerie is not open on Tuesdays so it will have to the Musee Rodin and you will have to get there right when it opens and as my son says bust a move. Are you planning to take the metro to the train station? I would because well, traffic exists. Metro line 13 stops at Varenne and Invalides both of which are near the museum and goes to Saint Lazare where you will catch your train. You can see how long the trip will probably take at www.ratp.fr -- be sure to change the time to a weekday at the time that you will be traveling and not the time where you are when you use their route planner. The Rodin does not accept large pieces of luggage but they do accept backpacks and umbrellas, etc. Perhaps you can store your luggage, assuming you have more than a backpack, near the station at City Locker (there is no luggage storage in Gare St Lazare) early in the morning and then head to the museum.
Edit: For the Arc d'Triumph, some say that the elevators are for persons with disabilities. It will not hurt to ask. I did not know that there was an elevator when I went in 2012 with my then 6-year-old-son and an employee waved at me and told me we could ride it up. My son was tired from walking all over Paris and I think the staff person looked at me and him and took pity on us. The elevator did not go all the way to the top. We had about 50 more steps. I have read that there is a second elevator to the top but I have not taken it. The monument can only be reached on foot via the Passage du Souvenir, a tunnel at the top of the Avenue des Champs-Elysées and at the top of the Avenue de la Grande-Armée via a staircase. Can you husband deal with that?

I think the attendants must keep their eyes open for people who look like they could use a little help, because that was my mom's experience at the Arc de Triomphe as well. She arrived with a regular ticket and had no idea there was an elevator until the attendant offered it to her for her ascent.

I wanted to take the elevator up the Arc but didn't see any signs. You go through security and then BOOM you're up the stairs, so you must ask BEFORE security to avoid the stairs. Good luck!