Oh my goodness, you have got yourself into a pickle
Calling children "brats" is not likely to go down well
Here is my advice, please take it or leave it
What you need to do is communicate your concerns to your daughter (primarily) amd your SIL
You need to explain that you love them and love spending time with them but perhaps a shorter visit next time as the extra noise and mess was tiring
Next visit you need to explain again your concerns about your grandchild and the dog before hand and ask that they handle any problems with their child quickly and explain to him how the dog should be treated. Also say that you will do your best to create a safe space for dog and child to be seperate when there is any chance they won't be fully supervised
And definitely apologise for the Google search, as a moment of frustration. Get that done as soon as possible, don't let it fester