In all cases, the difference between deductible work mileage and non-deductible commuting expenses are described in chapter 4 of publication 463. You need to look at the definition of "main place of work". If you have no "main place of work" for the dog and house sitting, then none of your mileage is deductible. If your home is your main place of work, then driving to other work sites is deductible. (Your home might be your main place of work, even if you don't have a formal office, you have to read the rules carefully).
https://www.irs.gov/pub/irs-pdf/p463.pdf
Mileage for your W-2 job is listed on the deductions and credits page under work-related expenses. These expenses are not tax deductible on your federal return for 2018-2025, but might be deductible on your state return (depending on which state you live in and other tax facts), so you can enter the mileage and it might benefit your state return.
Mileage for schedule C self-employment is reported as a business expense in the self-employment interview, and not on the general deductions and credits page. You can deduct mileage for your self-employment even if you can't or don't deduct W-2 mileage.
