Parents and child care advocates, yesterday, renewed their calls for better oversight of home day cares. There are a number of bills on the issue currently working their way through the legislative process; and child care advocates hope it results in stricter regulations. Supporters of reform want to see licensing —training and inspection standards — required for all home day cares; they also calls for background checks to be based on fingerprints rather than names. They are also urging tougher penalties against those who violate state regulations —but lawmakers are already indicating that compromise may be needed on some measures, in order to win approval on others.