The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or possibly your student has taxable scholarship income. You claim the tuition credit, or report scholarship income, based on your own financial records, not the 1098-T. You use the 1098_t as an input device. So, yes, you can, and should split the 1098-T. Put the box 1 $1695 on your return (and the $1393 computer/books/material) but put the box 5 $2740 on your son's return. And yes, sometimes the info goes on both returns.
Note: you are not both "claiming the 1098-T". You are the only one "claiming" the tuition credit. Your son is only using the 1098-T as a means for entering information.
Since all your expenses were paid by TAX FREE scholarships and 529 plans, you're not normally allowed to claim a credit (you didn't pay for anything with your AFTER TAX money). But the IRS allows you to reclassify those sources of funds in order to claim the credit. We're going to reclassify all of the scholarship and some of the 529 earnings as taxable income so that you can claim to have paid tuition and course materials with your (and your son's) after tax money. All legal and even suggested by the IRS in Publication 970.
My instructions above tell you how to do that and what results to expect.
