Because the two houses had declared a personal, but formal, war (or vendetta, or feud) with each other, it wouldn't be surprising to the other houses that H wanted to take out A.

Yes, the other houses could be suspicious that the Emperor invited A to Dune, knowing H would be upset. But the other houses could also think A had lobbied the Emperor for it as a way to fight H (getting rid of H's main money maker) in their personal war. As Archaea said, H was a sucky administrator on Dune, and the Emperor's profits were going down-- it was legitimate to believe the Emperor told H to step aside, that H had no ability to fight the Emperor's orders, and that the Emperor was willing to install A (a proven capable leader) in H's place-- their personal vendetta against each other was not a reason for the Emperor to make a poor economic decision vis a vis Dune.

Also, the other houses could also assume that A would turn down the offer if A suspected it was a plan by the Emperor to have H bump him off. (There's that whole dinner scene where you see some of the disparate powers, motivations, and assumptions by others on Dune who are politically connected). That Duke Leto didn't turn it down is one of the (multitudinous) philosophical points of the book. Was it the bull-headed-ness Leto inherited from his own father? Was it hubris, thinking that, knowing of the trap, he could properly prevent it? Was it a life-weariness, even a suicidal, tendency? Was it fate-- the universe out of balance, needing to create the circumstances that would cause Paul to grow into the person "it" needed?

That the other houses wouldn't accuse the Emperor of siding with H against A is explained by the Emperor's troops being held in universal fear. You don't fight against the super-power unless there's no other choice. If it's plausible to believe you won't be targeted by the evil power, the more prudent course is to lie low. (The Declaration of Independence says as much-- changing government is such a giant problem, most people won't do it unless there's no other choice.) (Or look at the Clintons-- everyone believes they've killed people that threaten them, but no one's made anything stick.) That's why Paul needed to 1) have proof the Emperor was in on it, and 2) have his own elite troops beat the Emperor's troops in battle, before he could creditably assert to others that the other houses would put aside their infighting over profits and power and unite against the super-power of the Emperor.

Also, from Paul's point of view, claiming the Emperor's daughter, i.e., right of succession, would be a reason Paul wouldn't want to immediately topple the Emperor's power (call him out), only curtail its use against himself and his interests (during the Emperor's remaining lifespan). Paul wouldn't want to immediately destroy the power he intended to inherit.

So, the book gives reasons why the situation is a little more complicated.

There are probably lots of other things going on, too. I've only read it once, and I haven't read any of the other books, so I'm no expert.