This is almost correct. It seems you missed an Other World encounter. Remember that the Arkham encounters and the Other World encounters are separate phases. Below is the correct sequence.
1. Movement. The investigator moves to the Witch House, where there is an open gate to the Dreamlands.
2. Arkham encounter. Instead of drawing an encounter card, the investigator is drawn through the gate and enters the first area of the Dreamlands.
3. Other World encounter. The investigator draws an Other World encounter card.
4. Movement.** The investigator moves to the next area of the Dreamlands.
5. Other World encounter. The investigator draws another Other World encounter card.
6. Movement.** The investigator returns to any location in Arkham with an open gate to the Dreamlands, and places an explored marker on that gate. When returning to Arkham, the investigator does not have to fight or evade any monsters guarding the gate. If there is no such gate open, the investigator is lost in time and space.
** It should be noted that the investigator does not receive any movement points in during this phase. Thus, he cannot use anything which requires him to spend movement points this turn.
I hope this helps. =)
Edit: Julia was faster. =P