Hamlet begins and ends with reference to Norway, Denmark's enemy. How is this conflict affected by what happens in the royal bedroom in Hamlet?
References to Norway may frame Shakespeare's Hamlet, but the conflict between Norway and Denmark is not in any way central to the play. The references provide background information in Act I (the king of Norway's death at the hands of King Hamlet, the threat of invasion, etc.), and catharthis and cleansing in Act V (the evil is destroyed and Fortinbras will stabilize the political situation in Denmark). Fortinbras also serves as a foil to Hamlet, of course. But, again, this political and military conflict is not central to the play.
Thus, you should probably think in terms of what this conflict contributes to the play as a whole, rather than think of what occurs in the royal bedroom contributing to this conflict.
That said, the one event that occurs in the royal bedroom that does affect the conflict between Denmark and Norway might be Hamlet's killing of Polonius. This moves Claudius to send Hamlet to England and order Hamlet's execution. The conflict between Claudius and Hamlet is in the "feeling out" stage before Hamlet kills Polonius. In other words, Claudius is not sure Hamlet is out to get him until Hamlet kills Polonius. The killing gives Claudius the excuse he needs to get rid of Hamlet, and the opportunity to have him executed away from Danish soil. The killing of Polonius might also lesson the high opinion the Danish people have of Hamlet.
In turn, Hamlet discovers the assassination plot and overtly returns to avenge his father. Thus, the king is preoccupied. He is worried about Hamlet, not Fortinbras. Claudius appears politically astute in the early acts of the play, but later he never considers that Fortinbras will disobey his orders and invade Denmark anyway. By the time Fortinbras invades, Denmark offers little resistance.
Other than that, the unseen sex between Claudius and Gertrude and the appearance of the Ghost probably do not directly affect the conflict between Denmark and Norway. Hamlet also berates his mother in her royal bedroom, but this has nothing to do with Norway.
If you must connect the royal bedroom with Norway, Polonius's death is probably your best bet.
Your question highlights the important wider political context of the play that must not be ignored by focusing on Hamlet's personal issues. Let us remember that the death of a King always heralds a time of great turmoil, and the way that Hamlet was in effect disinherited by his uncle and the hasty re-marriage of his father only heightens the sense of unease that looms over the play. We know that Fortinbras is out to get his revenge and sees this as an opportunity to win back territory that had formerly been lost. Note how Claudius addresses this issue in Act I scene 2:
Now follows, that you know young Fortinbras,
Holding a weak supposal of our worth;
Or thinking by our late dear Brother's death
Our State to be disjoint, and out of frame,
Collagued with the dream of his advantage;
He hath not fail'd to pester us with message,
Importing the surrender of those lands
Lost by his father, with all bonds of law
To our most valiant brother...
It is interesting that some critics present Claudius here as desperately trying to portray a confidence that he does not feel, recognising how his actions have increased the instability that Denmark is enduring.
Hamlet of course himself declares Fortinbras as his heir in Act V scene 2, recognising that with his death there is a power void that must be filled:
But I do prophesy th'election lights
On Fortinbras, he has my dying voice...
Thus we can see that throughout the play, the death of Old Hamlet and the re-marriage of Gertrude has repercussions that stretch far beyond the narrow sphere of Elsinore, and end in the annexation of Denmark by Norway.