Tax Question

Do you mean that you're co-successor trustees?  Are you also the only 2 heirs, and no one else is named in a pour-over Will, or the Trustee, as heirs? 

I assume your father has also passed, so both of the initial "settlors" (creators)  of the Trust are deceased?

Trust taxes are complex.   Are there any stock or mutual assets to be distributed?  I learned this year that they can offset taxes to the trust when distributed to the heirs, but I didn't really follow what the trust attorney told me.

I do know that if you haven't paid all the expenses of the last illness, the funds from sale of the house must be directed to those expenses.    

I'm in a somewhat similar situation.   Once the house is sold, and all last illness expenses are extinguished, the funds would be distributed to the heirs, of which I'm one.    At that point, I'll be reading the IRS 1041 booklet a few times to make sure that everything is handled properly, but I'll probably also ask my attorney (who handles trust taxation). just to be on the safe side. 

This is one of the forms that will be challenging my eyesight and brain:

https://www.irs.gov/forms-pubs/about-form-1041

And that's what I would recommend to you:   consult with a trust accountant.   I wouldn't take the chance - trust taxation is just so complex.

If it is a standard revocable trust, it is in their estate (and as PP said, unlikely you owe any estate tax).  As long as they were treated as the owner at date of death (through the trust), you and sis will take as basis the FMV as of date or death, or the alternative valuation date (I think 6 months after date of death), so minimal tax.  

To me, key is someone needs to file an estate tax return or probate papers to document that the estate owned the property on the date of their date.  If they gave it to you while they were still alive, even the day before they died, you are stuck with carryover basis (what they paid for it).    I am concerned that the trust was used to avoid probate.   Even if an estate tax return not due, you may want to file to document.

You need to talk to your tax specialist. I don't believe that you do.

If there is tax due on an inheritance it is normal for the estate to pay them. Not the person receiving the inheritance.

I believe that the current nontaxable inheritance amount is at roughly 11 million dollars for a couple, 5.6 for an individual.

You really should consult with your tax preparer because they have the entire picture.

You should consult the person that does you taxes.
In general any income is taxed.
If you spent any of your money fixing up the house to sell it you might be able to deduct your expenses though.
But a good tax preparer is your best bet for an accurate answer.