anyone with experience with Labradoodle Puppy Growling at children when resting or sleeping?

Hi All, My husband and I are looking for feedback regarding our 14 week old intact male labradoodle puppy. We have had him just about a month and overall he has been a wonderful addition to our family. We also have a 12 year old lab and three children ages 6, 4, and 2. Our concern is our puppy has growled at our two older children on three separate occasions while either sleeping or resting. Each has either gone over to pet or pick him up, and one time, he also nipped immediately following at our 4 year old. Each time this has happened, we have given the puppy a swift NO followed by a time out. We have also discussed with our children about giving the puppy space, not overhandling and so on, but they are children and they are bound to walk up to our dog and pet him at points. With that said, this behavior is unacceptable to us. I am wondering if anyone has had a similar experience, if it stopped at they aged, or what you did to curb this? Our older dog has never growled at a child or adult. This is very concerning to us. I am aware of the saying let sleeping dogs lie, but on a home with three young children, I have to be realistic. Any support would be greatly appreciated.