To get the 'Ask to Move in' interaction the other Sim has to think your Sim is either Sociable or Friendly. SO keep piling on those Friendly Interactions to boost their view of you!
I have never seen anything like this in my game, well I suppose I am limited by my play style of me staying on the lot and just using the buttons to send them to town etc. I really need to start exploring the town more and I may notice more things.