So the way that the will and Executor position works is that doesn't happen unless and until you go to probate court to execute the will.
This means although you don't need an attorney to make you the Executor, because you have already been declared the Executor in the will, it does take a judge to give you any powers as Executor. So although you could technically go to probate court without a lawyer, it could be difficult and it would be advisable to do so with a lawyer.
Now, you don't necessarily HAVE to probate the will. If there are no significant assets of your father, other than the home, you probably don't need to probate the will. Check the title to the property and see how the title was held. If it was in his name alone, it can go through intestate succession to the next of kin, so his wife first if there is one, and then to the children equally. Any bank accounts should say who gets that money, and there may even be someone else's name on the account. In that case that person would not have control over the account.
So you just need to take a look at what the assets are and evaluate if you even need to probate the will.
As for the tenant, you have to first check and see who owns that property right now. If the will says it goes to all the children, then your sister can legally collect rent. Again, unless you have an open probate case in court for the will, you are not technically the Executor yet. You have just been designated in the will as Executor, but you do not currently hold those duties, so the tenant does not have to send you the rent.
So figure out who owns the property now, and that will tell you who has the rights to deal with the tenant and collect the money.
Please let me know if you have any questions about this.