I need ideas on the best way to drive By public transportation

If you are asking for the best way to get from Paris city center to CDG by public transportation, the answer is to take the RER train from Les Halles or Gard du Nord. If you are outside of walking distance from one of those locations, take the metro to one of those stations.

Practically speaking, use Google Maps the day of to determine the best route, since it may change due to metro closures or delays. Also be sure to leave extra time since it is not uncommon for the RER to be delayed.

Since a metro ride is included as part of the airport ticket (14 Euro) you can save on the metro fare on the way to the airport by buying your airport ticket and using it on the metro ride to the RER station. I usually use the IDF Mobilities app on my phone to purchase Paris transportation tickets and use my phone to go through the ticket gates.

Use the RATP app for directions on your travel dates for up to date mass transit information. Google Maps is great for the walking directions but it is not always up to date on route closures.
Mass transit is the better choice to go from the museum to the Opera. You do not have to go back to the airport to get into central paris from the museum. The RATP app will offer you possible routes. You do know that the walk from the hotel to the museum will be well over an hour, right?

Hyatt Place Hotel walk to Musée de l'Air et de l'Espace

I may be misunderstanding but does this mean that you are planning on walking between Hyatt Place Paris @ CDG (241 Rue de la Belle Étoile, 95700 Roissy-en-France, France) and Musée de l'Air et de l'Espace (3, esplanade de l’Air et de l’Espace 93350 Le Bourget)? Looking at the locations of both on a map, it looks to be over 4 miles between them. More exactly, 4.3 miles/6.9 km. I'm a walker but that seems like a lot with luggage - which you'll have if moving from there to Opera in central Paris.

Again, apologies if I'm misunderstanding.

I agree with Kate. Walking to the museum seems impractical and time consuming, especially if you plan to bring your luggage with you. And while the Museum website says they have storage lockers for luggage and large bags, there is a size limit. So check your sizes carefully. It would seem most practical to take a taxi from the hotel to the museum. If you bring your luggage with you, then you would use the RATP app to find the most efficient combination of bus and metro to get to your Paris destination. If you leave your luggage with the hotel, you would need to return there, then go to the airport to get the RER or a flat rate taxi into Paris.

It would seem most practical to take a taxi from the hotel to the
museum.

I agree, and even probably without luggage.

Walking to the museum seems impractical and time consuming,

I wonder if it's even possible ! The autoroutes weren't made for pedestrians