In cfr §2635.502, paragraph (a) states:
(a) Consideration of appearances by the employee. Where an employee knows that a particular matter involving specific parties is likely to have a direct and predictable effect on the financial interest of a member of his household, or knows that a person with whom he has a covered relationship is or represents a party to such matter, and where the employee determines that the circumstances would cause a reasonable person with knowledge of the relevant facts to question his impartiality in the matter, the employee should not participate in the matter unless he has informed the agency designee of the appearance problem and received authorization from the agency designee in accordance with paragraph (d) of this section.
And in (b)(1)(ii):
(1) An employee has a covered relationship with:
(ii) A person who is a member of the employee's household, or who is a relative with whom the employee has a close personal relationship;
Now it may be that these laws do not apply to elected officials (IANAL and this may lead to another interesting question), but it seems that the VP should have recused himself from all dealings with Ukraine (or sought an exemption) as I believe any reasonable person would with knowledge that Hunter was receiving a substantial remuneration by a company that the Ukrainian government has regulatory control over, would arguably question the VP's impartiality in his ability to drive policy in that government and hence potentially benefit Burisma.
As a thought-experiment, imagine I was an elected US Federal Government official who was responsible for setting policy that could directly influence a company who was providing a new BMW to my adult daughter every month, for a task which she has no past experience, and which she does not seem to provide any valuable direct work product.
Am I wrong to believe that the GAO would rule that I should not be involved in forming that legislation while my daughter remained a recipient of these benefits specifically to avoid the appearance of a conflict?
Even if there is no known evidence of a conflict that is directly covered by the criminal code 18 U.S.C. § 209, the whole thing seems to wreak of the appearance of a conflict where the VP's close relative was receiving significant "remuneration" (scare-quotes because it's incredibly murky what work product Hunter was providing, beyond influence peddling) through a very short chain of high-level influence.