You need to have a look at Childminders: Information about Tax and National Insurance 2012/13 provided by HMRC Business & Education Support Team.
One of the allowable expenses is: trips and outings including fares, but exclude any cost relating to your own children.
For fuel expenses it says:
If you use your car in your childminding business, you can calculate your motor expenses on either a fixed rate per business mile basis or an actual cost basis.
Whichever method you use, you must you must keep a log of your business trips showing:
ï‚· date of travel
ï‚· destination
ï‚· mileage covered
ï‚· purpose of the journey.
Authorised mileage rate method
If the business is not VAT registered, childminders can use the authorised
mileage rates as a basis for their claims.
From 6 April 2012
Car or van: Rate for the first 10,000 miles 45p per mile
Rate after 10,000 miles 25p per mile
If you claim mileage allowance, no other motoring expenses or capital
allowances are claimed on the vehicle.
Read the guide for further information about motoring expenses.
You don't claim things from the parents. You claim them against your business tax, as you pay tax on your profit.
"Your taxable profit is your income from childminding (turnover), less allowable
business expenses and capital allowances for your equipment."
If you claimed the mileage allowance, then it is a business expense and so is deducted from your turnover, thus reducing your taxable profit.