If I were you I would embrace it. Get to know them, what they do, what they charge, what they don't charge for, sick days - stats - vacation etc. You will find a way to one up them. Be it hours, program, pay etc.

If you have 3 to choose from for every one opening then my guess is it's needed in your area! So I don't think you'll have a problem. The other thing I've noticed is the quality of food is not great in these bigger daycares so maybe that's what you want to emphasize with your ads. Either way, you've been established longer, you have a good client base, I'm sure you'll be fine.