Is it possible for my family and I to immigrate to the US?

When your U.S.-born child turns 21, he/she can file an immigrant petition for you and for your spouse (your underage children would become derivative beneficiaries of the petition). As parents of a U.S. citizen, you will be in the Immediate Relative category, not subject to any quotas and priority dates, so you will receive your immigrant visas within months from the date of filing the petition. One concern will be finding a co-sponsor in the U.S. with income sufficient to satisfy the then-current financial standards for an affidavit of support; alternatively, you would have to show assets worth, at least, 5 times the financial standard. Otherwise, you might seek an immigration venue through employment or investment, just like anyone else; your former status as an LPR and your child's birth in the U.S. do not give you any privileges at this time.

Your citizen child can petition for you and her siblings when she attains the age of 21. She must reside in the United States to submit the petitions.

If your child was born in the US, he is US citizen. For you, if you were deported by the immigration judge, you are barred from coming back for 10 years(it is unclear what do you mean that your green card was taken away).If you surrendered your green card, you may not be subjected to the 10 year bar. You can come back either on a visa or visa waiver program. However you cannot immigrate to the US unless you are eligible?under some provisions of the US immigration law, such as marriage, investors visa, employment based, etc.

Your US citizen child can petition for you when the child turns 21 years of age, and you and your family should be able to return to the US.