Hi there.
Thank you for your question. Children and puppies can often be a troublesome mix and i must say this problem occurs a lot.
The first thing i would explain to you is to never tell Alex off when Chester is around. As described in SitStayFetch the alpha order is very important in the household. If you tell Alex off Chester may feel that he becomes dominant of Alex which can make a huge lot of problems.
Often the easiest way to do this is to not let the child and the dog play together unless an adult is there. Alex may not want to tell the puppy off but you sure can. If you can limit how much time the two spend together (i know this will be very hard) while Chester is still nipping you have a much greater chance of solving the issue
Okay what i have described in other threads is what you seem to be doing which is great. Often talking to the child and telling them that they are the boss of the dog, the dog needs them to tell it off when it nips etc can make them feel very important. But Alex may not be interested in that
Remember that play can get out of hand and someone may get hurt. So be very careful with the two of them. Only allowed supervised play.
If Chester gets too much then you should reprimand him as you have been doing. If Alex gets upset or Chester continues then take Chester away. You will most likely end up with a screaming child but with time both Alex and Chester should learn what they should be doing
Good luck with both child and puppy and let me know how things go.
Kind regards
Todd Field