It's easy to point fingers - but at least @J cares enough for his children to want to try to re-unite his family as best as possible. The issue is not @j's character, but the two children, so shall we refrain from further muckraking and focus on the family?
As noted by @outsider - you're in an untenable position.
Without US citizenship or any proof of parenthood (birth certificate, hospital certificate with YOUR name on it somewhere, or something similarly useful identifying you as a legal parent and or guardian), the US embassy cannot and will not assist or intervene on your behalf. I seriously doubt they'll offer advice aside from "get an attorney" - and if you're extremely lucky - they MIGHT give you some dubious referrals.
The best solution is to try to negotiate with your estranged wife's parents or closest immediate family and let the family pressure the daughter into at least negotiating with you or negotiate on her behalf. You may want to start off with three (3) months of living expenses for her and the child (¥30k?) - but best to seek advice of an attorney first - if possible. She's already been in hiding for two months, so, assuming you trust her family - you may want to pony up some cash to smooth her life out - reduce the stress for all stakeholders - it's the right thing to do - but most US attorneys would recommend against this as it would set a precedent of ¥10k per month in child support and alimony.
In return, ask the family to send pictures (current or recent from the last two months) of at least your son so you'll know he's healthy and being treated well - but to be magnanimous - also try to get photos of your estranged wife - for the same reasons - you know she's healthy and all things considered, is well. Email, hard copy whatever.
I vaguely recall you mentioned something about HK a while back - so you may want to go with some reputable HK attorneys with certified licenses to practice in China. Chinese attorneys vary widely from mere paper pushing clerks to paralegal types - difficult to find true strategist attorneys aka attorneys with experience in battle plans. This will be expensive. I vaguely recall the Gates (Bill Gates' parents) family has a law firm in HK - Gates, and some other partners...but I'm sure they'll be rather pricey.
Good attorneys will strive for a reconciliation first - and with the fall back to divorce and or separation procedures as necessary.
I'm not sure why she took one child and left the other - but if she's the birth mother of both - that's an act of desperation. Your first actions will have to be lowering the stress level - so again, I suggest you begin with offering to provide a steady stream of financial support to her and your son through the parents - if they'll accept it - no strings attached (well - maybe just the "let's talk when you're ready" door) - then you're off to a good start - but it will be a long protracted process with no winners unless you can reconcile. Most single moms I met in Beijing were stubbornly adamant that divorce was their only option - but when conversations meandered - it was obvious some of their husbands really wanted reconciliation - so expect the worst - hope for the best.
As your second son is also not a US citizen - I'm sorry to inform you, you're in yet another untenable position - you cannot leave the country with him - that will definitely be considered kidnapping - so, now you're somewhat permanently anchored in china until this plays out or you manage to somehow resolve your second son's status. This will be extremely problematic for schools, insurance (required for school), hospital visits, etc unless you have his ID card and hopefully Hukou (family registration book?). This will be frustrating so a good attorney can help do many of these things for you. You may want to query the Aurora biz that advertises on here occasionally (search gokm for them). they may be able to assist with some of these things also - to include family attorney referrals.
You'll definitely need a reputable attorney familiar with Chinese family law, divorce, etc. They can also provide leads to detective or investigation services. If you use these kinds of services - ensure they are polite and non-threatening - and as nice and non-confrontational as humanly possible.
Regrettably - this is going to be rather expensive for you, regardless of how the scenario plays out.
Best wishes and regrets over your situation. I hope you're both able to eventually overcome this difficult time in life and ultimately re-unite happily for all concerned.