Looking at Melinda's activities prior to Trenton's disappearance, it doesn't appear that she is making any plans to "give him away" so she can get on with her life. It appears that life for Melinda and Trenton is "life as usual".
Melinda had plans for the future, she wanted to make a career for herself in law enforcement and she wanted to give the son that she loved a good stable home. Melinda always worked, and Melinda always took care of Trenton when she had custody of him.
Why would Melinda, who fought so hard for two years to KEEP her son with her, why would she "give him away" or worse kill him? Does it make sense? NO! So what other possibilites are there?
WHO was it that was always trying to get Trenton AWAY from Melinda? WHY was Melinda frantic to get her hands on thousands of dollars to PROTECT her and Trenton? WHO was threatening her? And WHAT WOULD MOTIVATE Melinda to jeopardize EVERYTHING she worked so hard to gain since she had Trenton?