Mueller is there to investigate SPECIFIC charges and to determine whether they have any basis or not, whether or not any of the findings are criminal in nature, not to do a proctology exploration just fishing around trying to find something not knowing what you seek to find! Anything Mueller investigates he needs to tie its relevance to the case and give good reason why he needs to look there, not turn up an unpaid parking ticket from 1994 and say: BUSTED! WE FOUND SOMETHING ON TRUMP!!
The best way to answer that is to look at what Mueller was tasked to do.
https://assets.documentcloud.org/documents/3726381/Robert-Mueller-Special-Counsel-Russia.pdf
The Special Counsel is authorized to conduct the investigation confinned by then-FBI Director James 8. Corney in testimony before the House Permanent Select Committee on Intelligence on March 20, 2017, including:
(i) any links and/or coordination bet ween the Russian government and individuals associated with the campaign of President Donald Trump; and
(ii) any matters that arose or may arise directly from the investigation; and
(iii) any other matters within the scope of 28 C.F.R. § 600.4(a).
It's important to look at that last one. because CFR states.
28 CFR 600.4 - Jurisdiction.
§ 600.4 Jurisdiction.
(a)Original jurisdiction. The jurisdiction of a Special Counsel shall be established by the Attorney General. The Special Counsel will be provided with a specific factual statement of the matter to be investigated. The jurisdiction of a Special Counsel
shall also include the authority to investigate and prosecute federal crimes committed in the course of, and with intent to interfere with, the Special Counsel's investigation,
such as perjury, obstruction of justice, destruction of evidence, and intimidation of witnesses; and to conduct appeals arising out of the matter being investigated and/or prosecuted.
So the question of can Mueller investigate obstruction of justice by Trump, the answer is HELL YES.