Need some advice on how to proceed with the situation:

We signed our part of the contract to buy a property, give 10% earnest money, but the owner is passed away without signing his part of the contract. Now, after 3 month, the seller's family telling us that other prospective buyers offering more and want us to raise a price.

Any ideas how to handle this situation?

Thank you.

Ask for your deposit back , see if they take your original offer

YOu deserve your money back, or try to get new seller to accept your offer.  Since seller never signed contract, you dont have a contract as far as I can see. 

It takes 2 to make a contract your contract wasn't valid with out both parties signature's

Yes. You either sweeten the deal or ask for EMD refund.