According to National Rail Retford has 84 parking spaces, Worksop has 100 and Woodhouse just 10. I would think that the car park at Retford is already very well used and probably gets quite full. Worksop has a large car park, for a relatively small station, and so there is some potential there. I’ve never seen Worksop station car park very full whenever I have been there. Looking at the small car park at Woodhouse, would anyone actually want to leave a car parked there, especially if they would be returning after dark.
Woodhouse less than 50k annual passenger entries, Worksop and Retford nearer 500k.
All westbound trains out of Hull stop at Brough. When I lived near Hull I never considered going to Paragon. Hull Trains know that will work similarly for them with south-east side of Sheffield residents using Worksop and Retford. (Similar effect at Dore for Manchester bound travellers from south-west Sheffield.)
I'm sure they wil pick up business but lack of frequency may go against them.
Pathing is going to be the critical issue. Services coming into Sheffield from the Meadowhall direction are regularly late, partially due to congestion, see;
https://www.recenttraintimes.co.uk/...tAvg=Mea&MetSpr=RT&MxScDu=&MxSvAg=10&MnScCt=2
Adding a few more trains a day through the throat from Nunnery probably won't make a major difference but they wouldn't help the cases for the restoration of a second hourly stopping train to Doncaster, the proposed hourly service from Chesterfield via Barrow Hill or the desired second fast trains to Leeds and Hull.
Platform space is another issue. The Hope Valley Capacity Scheme is about to deliver a second path between Sheffield and Manchester. Great, but there are now capacity issues in Manchester, Stockport... and Sheffield!
How many of the car drivers to London would be attracted away is hard to tell. I suspect not very many. Those wanting to be in central London will usually take the train. It's journeys to less central locations where the car scores.