"I wondered why it wasnt the total amount" " I am starting to think the reason the K1 says $77k is that was the income portion of the distribution (the rest would have been untaxable principal)."
Yes, that is very likely the case. The beneficiary does have to pay income tax on the earnings that are distributed but does not pay tax on the principal (or corpus) as that represents what was inherited, that is not subject to income tax.
In general, a nonresident does not owe state income tax on trust distributions unless the income was from a source in that state. For example, bank interest or stock dividends would not be from VA source even though the bank or broker was in VA.
But, if there was a business selling in VA or a rental property located in VA those would be VA source income.
Often there is no state source income that has to reported. Often when there is state income a K-1 for the state will be received as well as the K-1 for federal 1041.
Tax on accumulation distribution is reported on Form 4970.
"Beneficiaries who received an accumulation distribution from certain domestic trusts that were created before March 1, 1984, must file Form 4970."
"If you received a distribution for this tax year from a trust that accumulated its income instead of distributing it each year (and the trust paid taxes on that income), you must complete Form 4970 to compute any additional tax liability. The trustee must give you a completed Part IV of Schedule J (Form 1041) so you can complete this form."
You can check with the trustee to see if this was an accumulation distribution and to get the Schedule J part of the trust tax return Form 1041 if needed; but that does not seem likely from the description you have given.
Yes, you have a good understanding (but may need to verify with the trustee).
Please ask if you need more discussion or clarification.