[...] why it doesn't recognize it as a separate state, yet is satisfied that the PLO represents Palestine? I am really confused about this.
Hamas does care for the US recognition
For one, Gaza is ruled by Hamas, a religious liberation movement (unlike the PLO, which is a secular one), which does not even aspire to statehood in the western sense of the word. Hamas does not even accept the very principle of the negotiated settlement with Israel ("Two states for two people living in peace and security"), but demands that Israel disappear ("From the river to the sea"). Hamas does not show interest in joining to western bodies (like UN), abiding by western principles (like Geneva conventions), etc.
Weakness of the PLO
Exercising authority over its own territory is one of the core elements of being a sovereign state. Even before Hamas takeover of Gaza the Palestinian Authority was unable (or unwilling) to do so, despite the creation of a substantial police force allowed by the Oslo accords, which manifested itself as the Second Intifada . Thus, recognized as is, Palestine would readily become a failed state, being a state de jure, but not de facto:
A failed state is a state that has lost its effective ability to govern its populace. A failed state maintains legal sovereignty but experiences a breakdown in political power, law enforcement, and civil society, leading to a state of near-anarchy.
As an notorious example of state responsibility for controlling the terrorism originating from its territories one could mention the Assassination of Archduke Franz Ferdinand of Austria by members of Black Hand. While the role of the Belgrade in supporting Black hand is unclear to this day, the event served as a casus belli for the First World War.
Antagonizing Israel is a strategic loss for the US
Israel would obviously disagree, if Palestine is declared a state without having made a peace agreement with Israel. It is worth pointing out that Israel tried such unilateral moves itself when it withdrew from Gaza, leaving the Palestinians to try building statehood in the area without reaching a formal agreement - ironically, the move was much criticized by some Palestinian supporters.
The US recognition of the Palestinian state would likely lead to a rupture of the relationship between the US and Israel. The US would lose its strongest ally in the region, while Israel would lose its strongest political and financial backer. Certainly, it would be more damaging for Israel, than for the US, but not fatal - neither in economic nor in military terms. The most unpleasant likely consequence is that Israel would look for another ally - preferably a superpower with a veto right in the UN Security Council - in the best case scenario it would be the UK or France, like in the early days of Israel - in the worst case scenario it might be Russia or China.