Normally we oversubscribe panels quite a lot because the chance is remote that all circuits will be fully loaded at the same time. However when a single load is 60A and definitely will run continuously when it runs, that only leaves 40A for all the other circuits to share. That's a little bit small for that "oversubscribe" logic to really work.
You might consider making the subpanel 125, 150 or even 200A. There is nothing wrong with a subpanel being the same current as the main panel.
Since the subpanel is right next to the main panel, you don't need a main breaker in the subpanel. However if a subpanel does have a main breaker, its only purpose is a shutoff switch, so its breaker size doesn't matter (as long as it's not too small.) You might consider using a panel with a 200A main breaker, as a hedge against some future when you move all the circuits to that panel, and switch it over to become your main panel.
For that matter, with power company and inspector approval, you can lay it alongside and make both of them main panels under the tap rules. (this is how it's handled when an all-electric house has 400A service; they fit two 200A main panels).
Now back to your original question, about wire sizes, firstoff, the 6 AWG is out of the question, and I wouldn't use copper wires anyway for big stuff like this. I'd use aluminum. Really. The lugs on the panels will all be aluminum, and copper wires on aluminum lugs means dissimilar metals, differing expansion rates, galvanic corrosion, i.e. all the stuff that makes small aluminum wire scary. Aluminum is also 1/3 the cost and half the weight for the same ampacity.
Anyway, once you have decided your metal and ampacity, it's off to see the wizard to get the wire sizes. Put in 240V and 3% loss.** The wizard says for 100A, #1 Copper, or 1/0 Aluminum.
Obviously five feet of it won't cost much either way, but I would still favor Al because of the metal-compatibility issue with your lugs.
**Just to be clear, when you are doing long runs, also try it with 30% loss. That will force the tool to fall back on the minimum permitted size (irrespective of length), and will tell you what actual voltage drop you'd have if you used that. Often it'll be like 3.7% and you may decide 0.7% isn't worth spending $400 more on wire. Or you can play "what-if" until you strike a balance between cost and voltage drop. Won't be an issue in this case.
Best Answer
If you use a 100A breaker your main in the mobile home you will need #3 copper wire to feed the sub the sub panel. A 60 Amp breaker in the main panel should provide enough power from the loads listed this would require #6 copper wire.
You will need to run both hots a ground and neutral. In the sub the ground and neutral buses need to be isolated. Many times Panels come with the buses connected the connection will need to be removed or you can add a grounding buss screwed into the metal of the panel. (Make sure there is not a connection from the original buses to the box.)
I am hoping you will be living in the tiny house while remodel work is completed on the mobile. If both the mobile and the tiny house are used at the same time you may trip the main. If you trip the main you may have to do things like turn the AC off while the cook top is in use to prevent the main from tripping.