No, the President can't negate the 4th and 14th amendments via Executive Order.
But it is quite revealing that you wish he could.
Hmmm...what if we called it an "executive action"? Would that allow us to work around the Constitution? After all, isn't that what your boy Hussein did to enact DACA?
DACA was a policy closer to prosecutorial discression. The widely accepted principle that the Prosecutor can charge people based not on the letter of the law, but on the specifics of the case and how he feels the law intends to apply. Or the prosecutor can simply refuse to press charges, and there is nothing that anyone can do about it. Oh you can vote the Prosecutor out of office, but it is his discression.
DACA was a policy, the policy of the Federal Government was going to be that we were not going to pursue those people in court. We were not going to file for deportation, and we were not going to hold them. If we accept that the President is the Chief Executive, including over the Department of Justice, then Prosecutorial Discression can be directed by him. Nothing illegal about it.