No. Do not have him come back illegally. He will face a permanent bar.
You should go there to marry him. And then work with an immigration lawyer to get him back legally. Also talk to an attorney before going there to make sure that there aren't any other issues.
Dhenu Savla, Esq.
This answer does not create an attorney-client relationship and is not meant to be relied upon as legal advice.
Don't do it.
If he does what you propose he will have a lifetime permanent ban from the US.
You can fly there and marry him.
Then, you two can file a waiver application to shorten the 10 year bar.
Talk to an immigration attorney and don't do anything rash.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
You will most likely not be able to stop another deportation. He could even be prosecuted criminally for illegal entry after deportation. You mentioned health issues for one of the children and hardship to you - there may be grounds for a waiver that would allow him to return early. You should consult with an experienced immigration attorney as soon as possible.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.