IceAlisa -- I think this is one of those situations where someone needs to speak up. It may be enough that they do some investigation, or offer some parenting classes, or it may just go in a file until something else happens. But from the sound of it, it is more likely than not that something else will happen, and that child (and dog) deserve every chance to avoid abuses.
Yes -- to add to what mmscfdcsu said, in my state, if you were a teacher, and even heard one child say that another child had been given a black eye by a parent, you'd be required to make a report.
I am going to talk to someone who lives nearby to verify the bruise on the little boy story. I can't say it comes from a very reliable source so I'd like to confirm. But the choking of the Yorkie puppy is reliable and I believe it 100%, especially given how her last dog died.
"Nature is a damp, inconvenient sort of place where birds and animals wander about uncooked."
from Speedy Death
"When I was poor and I complained about inequality people said I was bitter, now I'm rich and I complain about inequality they say I'm a hypocrite. I'm beginning to think they just don't want inequality on the agenda because it is a real problem that needs to be addressed." - Russell Brand
I can't think of a reason not to report either case. It doesn't matter if it's hearsay or completely made up, reporting it can do no harm, not reporting could do a lot of harm. You only need to make a call, then you've done your part, the rest is up to the relevant agencies.
Report the abuse, sleep better at night.