Depending upon the value of the home you may want to look into a hard money loan. This may be a bit more expensive in the short term but in the long run it may allow you to effect the closing you desire.
However, do not misrepresent the situation or your intentions on any loan documents. Read your loan applications; a lender may have various forms of recourse if you lie on an application, including foreclosure. You don't want that.
It's always possible to rent out one of the properties for a short term (preferably a year, maybe slightly less...check with a lawyer or accountant) before making it your primary residence. But play by the rules.
Hope that helps.