My suggestion would be to charge them extra to bring them in early and charge them extra when they are late. I don't have any experience with Dog day care but with regular daycare's they charge about $10 - $15 for every 15 minutes you are late. As far as dropping off early I would suggest only in emergency situations. No offense but you need to get that back bone you mentioned. (If you are anything like me it is easier said then done.)I think you open plenty early to meet the needs of your customers, but that is something you have to decide.
I am a little confused? Do you have a second job? If you close at 3pm what are you doing until 7pm? The only reason I ask is because you might want to join a few business groups.(like the Chamber of Commerce or Womens League) In my area we have several different types of business groups to join wich are a great opportunity to mingle with other local business persons and get your name out there.