Yes, this is the RIGHT thread, and please don't apologize!!!!
Since the hour is late for me, relatively, I read your post rather quickly. There were several things that jumped out at me. First of all, small children should never, ever be left to "play" with a puppy unattended. It is a recipe for disaster. Whether intentionally or not, toddlers and even 3 year olds can be too rough with puppies, as can even a 7 year old. I would not blame this on the pup. The children need to be taught to respect the pup's space and to STAY AWAY! All interaction between the puppy and the children should be under the strictest supervision. Remember, this is but a short time in ALL of their lives! This is not forever, just for now.
You also mentioned that you "grab" the collar, or physically remove the puppy when he becomes nippy. You are giving him attention for this behaviour, good, bad or indifferent, he is effecting a response. Before I go too far, I really hope you read through this entire thread as long as it is, as every stage of development is touched upon and discussed herein. You may find several answers already available to you, which is why I directed you to here.
I noticed as well that the puppy becomes most nippy in the evenings, which is very common. Not unlike small children, he is overly tired, and overly stimulated. How else would expect a pup to demonstrate that he's had enough for the day if not this way? You also wisely pointed out that you attempted to remove his favourite treat, after 10 minutes in the evening, I believe. That is NOT the time for training with a high value treat.
As with our children, our pups have their own "witching hour" as well. They are cranky and worn out at the end of the day. Pointing your finger in your very smart puppy's face is simply inviting a nip. There are many other things to try first. One of which that you have not mentioned, is simply to stand up, cross your arms and turn your back on the puppy thereby giving him NO attention when he starts to nip.
Another tip, which you've mentioned that you do from time to time, is to give him something on which he can chew, and praise him. An ice cube, or a frozen, twisted face cloth works wonders for those sore gums. He is teething after all. You did say he was VERY SMART so that means he can learn. It is simply a matter of you finding the best way to teach him.
Please don't give up on this puppy! Your husband needs to learn some patience, dare I say.
Try to establish a routine that will eliminate the possibility of this happening. Since you know when your pup is most "cranky" and "nippy", perhaps try putting him in his crate, with a proper, safe chew item, like an ice cube when you wish him to calm for the evening.
Remember to praise, praise, praise the desired behaviour.
I've only touched on a very few basic things. Please take the time to read this thread, and by all means ask follow up questions. This is not the end...it is the beginning. Now is the time to really focus on this, and remember that some of the "drive" will most likely be tempered by having him neutered when that is age appropriate.
Again, I'm just giving random thoughts here as I read your post. When you push him away, point your finger in his face or grab at his leash/collar, you are engaging him. You must stop that and find another way.
Lastly, none of this is the pup's fault. He needs proper guidance and direction and you already sound like someone who is willing to do what it takes to make that happen.
Good luck....and do keep us posted. Enjoy the read!