Conventional Loan - Apply to 2 Banks?

[Maura Paler]

We are in contract for a single family investment property (vacation rental). This is our 4th VR investment property, will be our 3rd mortgage. 

We have been pre-approved by one bank (which is no guarantee of a loan we get that), but have found a better rate with another. We need to apply today as per the terms of our contract (within 5 days of signed contract - and we are heading out of town tonight!). 

Our first question is, should we apply to both banks ($500 application fee for each) to better assure a loan?  

Our second question is, we have relatives willing to guarantee the loan, but this would be a last resort we don't want to ask that unless the deal is ready to fall through - so if one (or both) banks rejects our application, and we add them as a guarantor, will that be considered a new loan and we have to start all over again, thus going over our 60 days to close contingency in contract? 

Our concern is that getting the loan will be tight, it was last time, as we have 2 mortgages already and high monthly living expenses (NYC) and we are both self employed. Banks scrutinized every penny and we have a very aggressive accountant. 

We are certain the property is right for our budget, is a good investment, so that is not in question. 

Any advise would be appreciated!