I agree with Sharnita. Folks seem to be acting very uncharitable toward the OP.
The way I'm reading it, one dog (who won't even be there past Sunday) got out and in the neighbor's yard, once. The OP believes she has fixed the situation. (Hence, "will do what I can." What more can
I also took the "call the landlord" thing as a way to deal with someone who just wouldn't believe her. I thought it was more polite and reassuring than just "well, I am," myself.
To address the question, I think it would be nice to introduce yourself to the daycare owner. I don't think I'd even bring the dogs up unless she/he asked ... if she/he does, then you can address it.
As far as the trailer, I agree with TootsNYC. It's a public street. Just get it out of there as soon as you can.
Good luck, OP.