How best to proceed will depend on the specific facts of your case. If the child is yours then you should truthfully disclose it. I suggest you consult with an experienced immigration attorney who can review your case and advise you how best to proceed.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.
All the things you mention will help. Amending her birth certificate if possible under Florida law (consult Florida family law attorney), take DNA test for all three and bring results to interview, file acknowledgement of paternity through Florida Family law courts and attorney. The most immediate and prompt solution is the DNA test, you can have results in 3-7 days and its 99% accurate. Consider hiring competent immigration counsel before you file, see my contact information below or choose other colleagues in this site.
The new company can apply for the H-1B anytime, no need to wait for April. And they can do the new PERM with the old priority date and the new I-140 at any time
I agree with my colleagues.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.