Can I claim the $250,000 capital gain exclusion on a 1041 federal tax return for when Settlor is still alive and qualifies for the two years in her own home before sale?

You can only claim the Section 121 exclusion if the trust is a grantor trust (i.e., treated as owned by the settlor).

Treas. Reg. §1.121-1(c)(3)(i):

Ownership and use requirements 

(i)Trusts. If a residence is owned by a trust, for the period that a taxpayer is treated under sections 671 through 679 (relating to the treatment of grantors and others as substantial owners) as the owner of the trust or the portion of the trust that includes the residence, the taxpayer will be treated as owning the residence for purposes of satisfying the 2-year ownership requirement of section 121, and the sale or exchange by the trust will be treated as if made by the taxpayer.  

Who then files the tax return?  The trust who would get the exclusion or the grantor on their personal 1040?  If the gain is less than $250k, does the sale need to be reported at all?  A 1099 was issued.