Wealth certainly does significantly influence relationships in As You Like It in as much as wealth creates jealousy, which leads to calamities such as attempts to murder and even usurpation. However, wealth only indirectly impacts Orlando and Oliver's relationship, while, though it is not directly stated, wealth more directly impacts Duke Frederick and Duke Senior's relationship. We learn of the impact of wealth on both fraternal relationships in the very first scene.
The desires for wealth influences Orlando and Oliver in as much as Orlando rightly desires the fortune their late father has bequeathed him in his will. However, what's more important is that Oliver is denying Orlando his fortune simply because he is jealous of Orlando's personal qualities, such as gentleness and intelligence. While the desire for his wealth leads Orlando to confront his brother, it is merely Oliver's jealousy that leads Oliver to be cruel to Orland and even threaten his life twice. Hence, wealth only indirectly impacts their relationship by providing the opportunity for Orlando to confront Oliver, which leads to further problems that stem from Oliver's jealousy.
Wealth more directly impacts Duke Frederick and Duke Senior's relationship as we can deduce it is one of the reasons why Frederick decided to rebel against his brother. However, we are actually never directly told why Frederick decided to usurp Duke Senior and must draw our own conclusions based on the parallel we see drawn between Frederick and Duke Senior and the two de Boys brothers. Shakespeare sets up this parallel by first introducing us to the problems between the two de Boys brothers and then in the very same scene using Charles the court wrestler to remind Oliver of the fact that Duke Senior has been usurped and driven into exile, as we see in the lines:
There's no news at the court, sir, but the old news: that is, the old Duke is banished by his younger brother the new Duke. (I.i.98-100)
Seeing the parallel helps us surmise that Frederick's motives for usurping Duke Senior stem equally from the same type of wrongful jealousy that drives Oliver to want to kill Orlando. However, unlike Oliver who is only jealous of Orlando's personal qualities, Frederick is most likely jealous of Duke Senior's wealth, power, and social status, showing us that the desire for more wealth is a main influence in Frederick's decision to mutiny and usurp his older brother from his birthright as duke.