I'm going to be pedantic on geography before anyone gets confused or actually lost.
The phrase "Southern Yorkshire Dales" was a bad choice from the company, the Yorkshire Dales National Park stretches across the West-Yorkshire and North-Yorkshire local government areas. The word dale shows the very old Viking influences in the north of england, and means valley, as does dal in most of Scandinavia. Yorkshire Dales (South) would have been harder to get wrong
The second line of the question just says Southern Yorkshire, and that is not where you will be in his tour (although you might get very close to South-Yorkshire on the Peak District tour). Any travel enquires you do for the Dales tour searching on Southern Yorkshire is likely to go wrong, but Southern Dales might work..
As for transfers between tours, the key is the start and end days, I've had a look and the are not all the same. If the end day of the Peak District or North Yorkshire Moors tours are the same as the start day of the Dales tour then they are quite easy to link, both start with a road transfer (Derby or Scarborough) then a train to Leeds and then the same train to Skipton. Rail journey around 2½ hours, transfer to railway 30-60 minutes. Dorset and South Downs are probably too far but Dorset scenery would be a very good contrast to the Dales as well as less chance of rain! Would it possible to find a Dorset tour that ends the day before the Dales tour starts and spend one night somewhere in between?