1. Go on Wednesday
I would try to do this on a Wednesday, since this is the day in which both the Rodin Museum and the Louvre are open late. The former closes at 20h45, the latter at 21h45. This is to maximise the time available to get this trip done, thus reducing its time-criticality.
2. Reserve your Tickets
I can't stress this enough: reserve your museum tickets in advance to avoid most queues. The Wallace Collection is free (gotta love the UK). Rodin Museum tickets can be booked here. Louvre tickets can be booked here.
3. Wallace Collection -> Eurostar
The Wallace Collection opens at 10h00. You obviously want to be there as soon as it opens. Once in, go to the first floor and aim for West Gallery III. Assuming it takes you one hour to get to the painting and admire it in its full glory, you should be out of there and into a taxi by 11h00.
You'll then be on a taxi for 16-17 minutes towards St Pancras.
Once there you could either get the the 12h24 train to Gare du Nord. This leaves you enough time to check-in, go through passport controls and drink an extra-hot skinny hazelnut frappuccino whilst waiting for the train.
4. Gare du Nord -> Musée Rodin
You'll arrive in Gare du Nord at 15h47. From there you either take a 25-30 minutes taxi ride to the Musée Rodin. In alternative, you can use any RATP combination available including (ordered by closeness and number of changes):
- Line 2 to Place de Clichy -> Line 13 to Varenne
- Line 4 to Strasbourg Saint-Denis -> Line 8 to Invalides -> Walk
- RER B to St-Michel Notre-Dame -> RER C to Invalides -> Walk
- Bus 54 to Plache de Clichy - Caulaincourt -> Line 13 to Varenne
In any case we are looking at an average 50-60 minute journey. You'll get to the Musée Rodin at 16h30/17h00 on average.
5. Musée Rodin -> Louvre
Now it's 17h00 and you have 3 hours before the Musée Rodin closes, and 4 before the Louvre does. Plenty of time to see what you want to see. Having pre-booked the tickets means that you do not need to queue with the rest of the visitors. Head to the sculpture, gaze at it with awe and wonder, let your eyes sparkle. I'd say you'd stay one full hour in the museum to fully enjoy the experience.
At this point it's 18h00. You need to get to the Louvre. You can take a 13-14 minute taxi ride to the museum. Or you can spend 20 minutes in the metro taking:
- Line 13 from Varenne to Chaps-Elysées-Clémenceau -> Line 1 to Palais-Royal (Musée du Louvre)
6. Sneak in the Louvre
Here is the interesting part. It's now 18h30, the museum closes in three hours. Three hours I tell you! More importantly, since you pre-booked your museum tickets, you can use the entrance at Passage Richelieu and beat the crowds:
Say that it took you 30 minutes to locate the entrance, get your bags checked and descend in the Louvre. You now have 2h45 to find Francesca da Rimini and Paolo Malatesta Appraised by Dante and Virgil. The painting can be located on the first floor of the Denon Wing, Room 77:
Given the Louvre map, all you have to do is cross the louvre from the Richelieu wing to the Denon wing, and then take go up two floors from -1 to 1.
Hey it's not 19h30 and you have two hours and some spares to admire you painting. This also means that you have plenty of spare time in case you were delayed at the Rodin museum or on public transports.
Louvre -> London
Unfortunately it seems you won't be able to make it back to London on the same day since the latest outbound train from Gare du Nord seems to leave at 20h01. That's not a problem, find a bistrot, have some dinner and use their wifi to book an accomodation.