as to the refi. any amount over and above the mortgage balance on the date of the refi is not personal residential interest so it does not go on schedule A. the cash out to the extent used to acquire rental property goes on schedule E under the IRS tracing rules. The deductibility of any cash not used on the rental depends on what it is used for. -if personal the interest is not deductible.
also the interest deductible allocable to your home may also be limited if the mortgage balance at the time of the refi exceeds the respective cap
