Thank you all for the replies.

The reason I sent him to the second day care is the cost. Because it's cheaper and includes food, it's hard to get a spot. I've been on their waiting list even before bub was born. The first day care wasn't my first choice, but he's been there long enough and he's pretty settled there. Now he has to go through the phase again. I feel guilty to put him in this situation. But as you said, as long as it's once off, i shouldn't be worried. He only goes there once a week and three days in the first day care. So I think he can take the second one as just another place to play.
Eventually, I will choose one center so I will see he's happy in the second day care first. Hopefully he will be, so it can save me a bit.
Thanks again for all your advice.