Beware the Limits on IRA Rollovers
According to IRS Code Sec. 408(d)(3)(B), a taxpayer can only make one tax-free rollover contribution during a one-year period. If the taxpayer takes advantage of this a second time, even within the 60 day allotted time period, will have some unfortunate taxable consequences. Before 2015, the one-per-12-month rule could be applied to each separate IRA you owned.
The distribution you intended to put back into the tax shelter will instead become taxable. You will incur tax penalties for excess contributions as long as the disallowed money remains in the IRA.