Well, for one thing, I wouldn't allow your child to touch the dog in such a way. Think about it - if someone was playing with your eyes, wouldn't you be more than a little irritated? Dogs can't say "stop that, please" in human language. They can only say it through dog language. Your dog's response sounds 100% natural to the incidents.
Also, whenever you have a baby or young child - you should NEVER leave them alone with a dog. Regardless of whether you have had that dog for months or years. I mean, I have a GSD. I trust him with my life. I have no fear about him being alone with a baby or a child. But, I will NEVER leave him alone with a baby or a toddler. Because no dog is 100% and no toddler or baby knows how to approach dogs in the right way.
In terms of the feeding issue - easily fixed by feeding the dogs in different areas. This is actually a common problem in multiple dog households, especially when introducing a new member to the family. Food is a resource, and it's a potential fight waiting to happen. So, feed in separate rooms: either one dog eats outside, and the other inside or feed them in their crates. Etc.
To me, these issues don't raise red flags. Your pup is young, and will be a puppy for awhile yet. Moreover, he's still new to the household and probably still in an adjustment period. I would do NILIF, I would feed the dogs separately, I would never leave the dog alone with a child, I would make sure the dog had enough exercise, and I would work more on teaching the 19 month old how to approach dogs and how to touch them. Your other two dogs may be used to the 19 month old and OK with her petting them in the way you described. But, this is a 9 month old lab - whole different story, and I definitely would not allow any eye poking or any petting that isn't appropriate.
However, obviously, if you don't feel the dog is a good match - call up the rescue.