Hello and welcome to JustAnswer. Please note: This is general information for educational purposes only and is not legal advice. No specific course of action is proposed herein, and no attorney-client relationship or privilege is formed by speaking to an expert on this site. By continuing, you confirm that you understand and agree to these terms.
I am sorry to hear about your situation. What essentially happened is that you received a B2 visa while your I-130 was pending. You then traveled on your B-2 visa to USA, and overstayed, living in USA for 18 years without proper status.
Needless to say, this has earned a ban of 10 years from USA for doing so once USCIS figures this out. USCIS processed the I-130 but due to the overstay, they may disallow it because of the 10 year ban (for violation of the overstay on the B2).
The best way to resolve this is perhaps file an I-601, which is a WAIVER of inadmissibility. See here:
Such a waiver can ask that the ban be waived based on the fact that not being able to enter would prove an"undue hardship" to a US Citizen (who in this case can be the children). Then, it is at USCIS's discretion whether or not to grant the waiver. If it is not granted, it may be administratively appealed and eventually appealed even to the US District Court.
Using counsel here is strongly recommended as this matter can become very complicated, very fast. If finances make this hard to do, I can provide a list of pro bono leads if you want me to - simply let me know. Good luck.
Please note: If I tell you simply what you wish to hear, this would be unfair to you. I need to be honest with you and sometimes this means providing information that is not optimal. Negative ratings are reserved for experts who are rude or for erroneous information. Please rate me on the quality of my information; do not punish me for my honesty.
I hope this helps and clarifies. Please use the SEND or REPLY button to keep chatting, or please RATE when finished. You may always ask follow ups at no charge after rating. Kindly rate my answer as one of TOP THREE FACES/STARS and then SUBMIT, as this is how experts get credit for our time. Rating my answer the bottom two faces/stars (or failing to submit the rating) does not give me credit and reflects poorly on me, even if my answer is correct. I work very hard to formulate an informative and honest answer for you; please reciprocate my good faith with a positive rating.