You cannot have both the child tax credit and the foreign income exclusion because of recent legislation. Your wife would needed to have utilized the foreign tax credit I am sure someone will come along and correct me if I'm wrong but that is how it works.
No news is good news with the IRS. Don’t worry about a lack of response. You can always call if you are worried. I called after 3 months and they were able to tell me.
In your wife's circumstances, I would keep my foreign born children out of the US tax system until they were at an age that they can decide themselves. Unless there is law change, they will have problems living overseas as US citizens, retirement savings, job prospects, Fatca and they would have never received a single benefit from the USA being born abroad. In future if they want to take up US citizenship, go work, study, live in the US, they always have that option.