The team may be correct to blame Peter for the extent of the problems; however, this is unknowable from the information given. Peter could perhaps be faulted for overselling the ease of using Product A, rather than managing the expectations of his team, and preparing them to expect difficulties, and framing the problems as simply challenges the team must work through to achieve success.
It is also possible Peter could be guilty of not properly equipping the team to succeed with his chosen Product A, such as getting expert consulting in implementation of Product A and training his team.
It is not necessarily proven or provable that Product B would have been a better option for the team, because humans are involved. However, for the purpose of discussion let's simply accept the premise that Product A was in fact the better choice. Given that, team members are potentially guilty of several logical fallacies in blaming the problems with product A on Peter and his decision to go with it over Product B, and particularly in assuming B would have been a better choice.
Fallacies from the perspective of a team member blaming Peter:
Argument from ignorance: "Product B would have been better." (but without having direct experience with B, thus coming from a place of ignorance)
Correlation proves causation: "Peter chose Product A over Product B, therefore Peter's choice of Product A is to blame for the problems we are experiencing with A." The causes of the problems, perceived or real, are not stated and are not possible to know without informed research. (Some organizations would use tools like "5 Whys" to attempt to discover the root causes of the problems.) Problems may have resulted from incompetence (or even sabotage) by team members, by lack of followup from Peter, or the problems could simply be the "normal" rate of problems being perceived as "excessive".
A Latin name for this fallacy would be "Post hoc ergo propter hoc" meaning "after this, therefore because of this".
In the category of Faulty Generalization fallacies, there are several more that potentially apply.
Cherry picking -- pointing out obvious individual issues and problems with A, while ignoring or even suppressing evidence that B may have had the same problems or even worse problems.
Hasty generalization -- basing sweeping conclusions on a small sample size. There are problems in initial use of A, therefore it was a bad decision, and Peter made a poor decision in choosing A. The real causes could include such possibilities that Product A has a learning curve for effective use, or that Product A has a best practice installation procedure that was not followed. Peter could certainly be culpable on these, just for a different reason than simply his choice of Product A.
An influential team member could lead others astray with the fallacy of Misleading vividness, presenting isolated, non-showstopper problem(s) with such vivid, emotional detail, as to overly influence and mislead the team over minor problems.
Peter may or may not have been guilty of a False Dichotomy fallacy in limiting the choices to A or B. I think it's reasonable to give him the benefit of the doubt and surmise that A and B were his top two choices out of possibilities considered.
In practice, Peter would be poorly served to spend much energy looking for logical fallacies in the team's reasoning. He would be far better off working with the team to identify and break down the problems encountered with A, and to engage the team in working through these problems, and to ensure he has done all he can to provide the necessary implementation, training, and support resources to make Product A a success in his environment. Effective leadership would trump philosophy on this one.