With respect to the Section 121 exclusion ($250,000 or $500,000 if married filing jointly), you and your brother will qualify if both of you own and use the home as your main residence for two of the last five years leading up to a sale.
You and your brother will also qualify for the $500,000 exclusion provided you and your brother own the home for two out of the last five years leading up to a sale and you and your brother and your wives use the home as your main residence for two of the last five years leading up to a sale (your spouses do not have to own the home or otherwise be on title; they simply need to use the home as their main residence).
See https://www.irs.gov/publications/p523#en_US_2019_publink10008996
Gain subsequent to the 2008 tax year (starting January 1, 2009) would also have to be allocated between qualified and nonqualified use per Section 121(b)(5).
With respect to the gift, your father will most likely have to file a gift tax return (Form 709) although no gift tax will be due unless your father has exceeded the lifetime gift tax exemption of $11.58 million.
You and your brother will, however, take your father's adjusted basis in the home, which will include the depreciation deductions allowed (deductions he has taken) or allowable (deductions he should have taken) during the time the property was held for rental use and there will be a recapture event when you sell the property (i.e., you will not be able to exclude the allowed or allowable deductions from any eventual gain).
In fact, you and your brother will have a split basis if the fair market value of the property at the time of the gift is less than your father's adjusted basis. In that event, your basis depends upon whether you have a gain or loss on an eventual sale. . Your basis for figuring gain is the same as your father's adjusted basis plus or minus any required adjustment to basis while you held the property. Your basis for figuring loss is its fair market value when you received the gift plus or minus any required adjustment to basis while you held the property. If you use your father's adjusted basis for figuring a gain and get a loss, and then use the fair market value for figuring a loss and have a gain, you have neither gain nor loss on the sale or disposition of the property.
See https://www.irs.gov/publications/p551#en_US_201812_publink1000257002
Otherwise, if the fair market value of the property at the time of the gift is equal to or greater than your father's adjusted basis (which is more likely), your basis is the donor's adjusted basis at the time you received the gift.
You might want to seek local professional legal and tax counsel for this matter before proceeding.
