Note that this same President who claimed he had unfettered discretion to ban Muslims from the U.S. by executive order, now claims that the former President did not have the same constitutional power to exercise prosecutorial discretion on behalf of dreamers. In fact, over 100 constitutional law professors signed on to a letter at the time affirming the constitutionality of the DACA action. [legal argument at https://pennstatelaw.psu.edu/sites/default/files/documents/pdfs/Immigrants/LawProfLetterDACAFinal8.13.pdf]. Article at https://www.dailykos.com/stories/2017/8/16/1690348/-100-law-professors-to-Trump-No-question-DACA-is-constitutional.
Look at it this way. If you are stopped for speeding, does the officer sometimes not write a ticket but give you a warning instead? That is an exercise of prosecutorial discretion and it is available in all areas of enforcement. When Pres Obama decided to prioritize removal of some aliens and not others, that is within his authority. If Congress doesn't agree with it, they can pass laws and appropriate the necessary funds to accomplish the desired result. Since they have not appropriated the necessary funds to remove everyone here without authorization, the enforcement bodies have to prioritize their enforcement actions. Surely, no one thinks that deporting non-criminal immigrants brought here as children should be our highest priority.
It is also sadly ironic that the President who seeks security in the Constitution for his inhumanity is the same person who gladly pardoned convicted criminal, Sheriff Joe Arpaio, whose crime was defiance of a court order pertaining to his unconstitutional treatment of unauthorized aliens. If it is the Constitution you care about, you don't show it by pardoning someone (even before sentencing) who proudly violated it.