わたしの いえ＿ へやが みっつ あります。
Essentially what I'm trying to say here is, "There are three rooms in my house"... What should go after ie (house)?
It would be best to denote the house as both the location (of the rooms) and the topic of the sentence by using both.
In my house [←topic], there are three rooms.'
Colloquially: 'There are three rooms in my house.'