China – Chinese travel permit

My Chinese wife, two children (Schengen nationals) and me (also Shengen nationals) will be traveling to China soon.
Applying for a Chinese visa is quite expensive: for us three, the cost would be almost 375 euros.

It seems that there is also the option of a Chinese travel permit (for children) that seems to be more affordable.

I'm just wondering if I'm afraid that my children will be considered Chinese nationals by the PRC authorities. Were there negative precedents?