Don't be so harsh with people who are trying to help you. Telling you to send the wife and children back to their native country to apply for visas is not deportation, a legal court order. Having the wife and kids leave is a voluntary act in compliance with immigration laws. Foreign citizens who enter with visas and overstay may be able to adjust status to a green card in some cases, but those who enter illegally cannot. They must leave and re-enter legally. That is the law.
If the children entered with visas and overstayed, you don't need to adopt them and I don't think you can if they're here illegally anyway. You can petition to adjust their status to a green card while they stay here in the US. If they entered illegally, they need to return to their country of citizenship and re-enter with immigrant visas.
P.S., I'm pretty sure most respondents to your question were born in the US, not Europe. You appear to confuse citizenship with ancestry. Your wife and stepchildren are not being told to "go back home" because their ancestors were not American, but because they are foreign citizens who are not here legally.