Can I legally and solely claim our son on her taxes?

I'll assume that the issue of who can claim the child is not addressed in your divorce/separation agreement. That being the case, the parent who resided with the child for more than half the year would be entitled to claim the child. If the child spent more days with her than with you during the year, she is entitled to claim the child.

The child must be a "qualifying child" according to the I.R.S.'s rules regarding claiming a child as a dependent. In general, to be a taxpayer's qualifying child, the child must meet the following elements: Relationship - the taxpayer's child or stepchild (whether by blood or adoption), foster child, sibling or stepsibling, or a descendant of one of these.Residence - has the same principal residence as the taxpayer for more than half the tax year. Exceptions apply, in certain cases, for children of divorced or separated parents, kidnapped children, temporary absences, and for children who were born or died during the year.Age - must be under the age of 19 at the end of the tax year, or under the age of 24 if a full-time student for at least five months of the year, or be permanently and totally disabled at any time during the year.Support - did not provide more than one-half of his/her own support for the year. If a child is claimed as a qualifying child by two or more taxpayers in a given year, the child will be the qualifying child of: the parent;if more than one taxpayer is the child's parent, the one with whom the child lived for the longest time during the year, or, if the time was equal, the parent with the highest AGI;if no taxpayer is the child's parent, the taxpayer with the highest adjusted gross income (AGI).Based upon the fact that you get the child two weeks out of the month, the child will typically live with you for less than half of the year. Thus, your ex-wife appears to be in a position to claim the child, as the child spends more than half of the year at her residence.