Lenders are very concerned with people doing exactly what you said, so even if your could qualify for the second mortgage, they will proabably look very closel st your other home.
Your best bet would be to rent out he home you are upside down on, then hopefully you will be able to qualify for new home using the rental income.
You would be better off continuing to rent until you first home until you are no longer upside down and can sell it. A short sale makes it nearly impossible to get another mortgage for 2 years and then you will probably only qualify for a sub-prime loan with high interest rates. Your credit will be impacted for 7 years after the short sale.