Hiya Peter! Welcome to the Crunch Chorus Community Forum!
If by ‘SDC’ you mean Supervision, Direction and Control (assuming so!), then this situation applies regardless of your business structure (sole trader or limited company).
HMRC defines ‘SDC’ in the context of its agency legislation. You can read more about this in our article. Please be aware the ‘SDC’ test is based on your assignment working practices and any contractual terms.
If you want to claim mileage expenses, this cannot be to your normal place of work. Mileage can only be claimed when attending a temporary work location. You can read more about this in our guide to business expenses for a sole trader.
It may be worth booking a call with one of our advisors to see if Crunch can help with your IR35 issues.