Your best bet (ha, ha!) might be to contact a local child-minding agency (see local Yellow Pages), harry, to see if they can send round a child-minder to your house for the day. Additionally, local pre-school playgroups may be able to put you in touch with a respectable sitter, or even a mum who wouldn't mind another two tinies for a day. Another idea is to put an ad in your local paper for a babysitter for one day only, references required. The sitter can then sit the babes at home, give them their food, change the necessaries, etc., and can have all the mobile numbers to hand.
The creches at racecourses aren't really for babies, they're for slightly older kids, and the nappy-changing facilities tend to be in the women's loos! So you'd be better off having complete peace of mind with someone sitting for you professionally at home.