The exemption for counting days for the substantial presence test id for 2 calendar years, so 2014 and 2015. If she had a treaty exemption, that would be valid for 2 years if the treaty as an exception to the savings clause (which must be claimed on the tax return).
So for 2016 she would start counting days January 1st, not July. The same goes for the J2 dependent. For the 2016 tax return you count all days of presence in 2016 (not the days in 2017 and 1/3 of days in 2016). So if they both were present in the US January 1st 2016 and stayed the whole year, they would meet the test and be resident aliens.
If the treaty with her country as an exception to the savings clause, you need to claim that and it's best to use form 8833. All income she had from January to July has to be reported, but can then also be entered as negative income, if the treaty still exempts it.
