Some thoughts:
Not every asset needs to be divided 50/50. If your father has significant other assets besides his house, maybe you could inherit the bulk of those and your brother could inherit the house. For example if he has a $250k house and $250k in investments, then he could get the house and you could get the investments.
A trust to be used to pay the property taxes is a fantastic idea, assuming the assets are there to cover it, especially if the property could be divided. If the inheritance is enough, it might be a good idea to name a third party (bank, brokerage, attorney, etc) so that they are taking responsibility for the administration and management of it. If not, and you are going to be the trustee, make sure that the trust is very specific about which types of investments are appropriate and in what percentages. If the trust is not able to pay the taxes indefinitely, then you want to make sure you have protection against liability when the money runs out. Trustees can be sued for mismanagement of trust assets.
Just because you are a named beneficiary doesn’t mean that you have to accept the assets. Every state will allow a beneficiary to refuse the inheritance. You could also accept the inheritance, pay the inheritance tax out of that and then gift the assets to your brother, either directly or through a trust.
In any case, a good heart to heart talk with all parties would be the best thing at this point. Get everyone together, stock up on the preferred beverages and snacks, and hash everything out. Maybe your brother has an unrealistic idea of how much he will be inheriting. If he thinks that he’ll be getting a ton of money and a free house when your father passes, the reality may create ill will (“I was supposed to be all taken care of when dad died, but my asshole brother screwed me out of it”). Surprise inheritance issues can amplify deep seated negative feelings and resentments or even create them. When everything is known beforehand, you tend to not run into those issues.