No the children are not qualifying relatives and they are not 21 so they are not old enough to petition for you. Based upon what you stated you would not have a case to return to the US.
Legal disclaimer: The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.
Based on the information you provided, it appears that, in order for you and your wife to be able to enter the United States again, you and your wife would need to be the beneficiaries of a valid immigrant visa petition, or otherwise be eligible for some sort of visa, whether it be based on employment, study, or even a visitor visa.
It appears that you might not have any family members who could file an immigrant visa petition for you at this time. You would need to have a petition filed by your US Citizen children ages 21 or older, your US Citizen siblings, your US Citizen parent, or your Permanent Resident parent.
For the other types of visas, you would need to investigate to see if you might be eligible.
It is not clear from your posting - did you and your wife accumulate unlawful presence during your time in the United States? If you did, then you might ALSO need a waiver of that unlawful presence. If you need such a waiver, you would need to show extreme hardship to your US Citizen or Permanent Resident parent(s). It appears that you don't have a parent who is a US Citizen or Permanent Resident.
I suggest that you consult with an experience immigration attorney, who would be able to ask you all of the relevant questions, and to give you a legal analysis based on all of the facts.
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I agree with my colleagues. Children are not considered qualifying relatives for purposes of a waiver. Also, they cannot petition for you until they reach the age of 21. You've got a lot going on here and in order to advise your appropriately a lot more detailed information is needed. I would advise you to consult an immigration attorney about possible options that may be available to you. Good Luck.
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The hardships are not your problem. Your problem is you need a qualifying relative who can sponsor you. Since your wife is not a USC, your children will be able to do so when they turn 21.