Gee,
Quote
the project engineer specified the laterals on plans. Later admitting that they resized the MDP during the design and forgot the increase the service laterals.
The engineers later asked for change order pricing to increase to 4 sets #500MCM. thats where I got the #500).
the engineer admits his mistake here and does the right thing by asking you to submit a change order.

Quote
Now the owner has said he will not approve any additional funds. So the engineer has stated my change order request will not be approved.
So now he is in effect saying, "my mistake will come out of your pocket, not mine".

The engineer has Errors and Omissions insurance that would cover his mistake if he can not come to an agreement with the owner.

Whatever happens you should not entertain the thought of making the correction at your expense even if this strains your relationship with this engineer.

Roger