The 1099-R for the direct transfer shouldn't have been issued ... but since it was, you'll show it as part of the gross distribution amount on form 1040 line 16a.
Also on 16a will be the second 1099-R, that you took out.

Hopefully, the 1099-R shows zero in the taxable box ... ?

Save all documentation on the rollover of the 401(k). The IRS may ask you to produce it.

First question - can a Simple IRA be rolled into a 401(k)? Yes.
First issue - the Simple is supposed to be open at least two years before any distributions, else they are subject to 25% penalty.

Second issue (the easy one) - the IRS isn't good at tracking indirect rollovers. Provide them with a copy of the rollover deposit into Vanguard.

The amount rolled wouldn't show on a 1040-X, and you would need to do a detailed explanation of what was rolled, when, and "see attached confirmation from Vanguard." The penalty for early distribution from a Simple IRA would show, it's calculated on a 5329.

Not sure if this is one of the penalties the IRS is hitting you with, or not.

Are you sure you don't want to get some professional assistance with this?