Your "unique situation" is much too complicated to handle here in an online forum, and there is a great deal of information missing. You need a lawyer to clarify exactly what is owned, who owns it, what is or is not in the estate, who inherits what, and what the tax effects are. You might need both an estate lawyer and a tax lawyer.
You have mixed up past, present, and future tenses, so it's hard to tell what has already happened. It seems like you might have already sold the property. Also, among many other loose ends, it's not clear whether ownership was actually transferred to you before the sale.
If the property was given to you before the owner passed away, you did not inherit it. It was a gift. (And a gift tax return will have to be filed on the giver's behalf.) Your basis for a gift is the previous owner's basis, which is probably what he paid for it. In that case, your taxable gain is the increase in value from when he bought the property. But if the father retained a right to live in the home, the gift might not have been completed. This is one of the things you need a lawyer to clarify.
If you were actually the sole owner of the property when it was sold, all of the proceeds of the sale, and all of the capital gain, are yours. If you choose to give some of the money to your siblings (half-siblings?), that is gifts from you to them. But you cannot give them the capital gain.
If there was not actually a completed gift to you, and the property legally remained in the estate, there will be little or no capital gain, and therefore little or no tax. That's because the basis of inherited property is the fair market value on the date of the owner's death.
But everything I've said is just background information and speculation, because the details of the situation are very unclear. So don't rely on what I said. Get a good lawyer.
