@Metior_Ice - thanks - that helps a lot - I will experiment with judgements
@Atreya33 - the interactions "move-in" and "join household" appear when a Sim is growing a friendship (the green bar in relationship). When growing a friendship with an Island Elemental it is important to grow the friendship - not romance.
1. Sim will summon Elementals - introduce and grow friendship
2. Look for the interaction "hang out" so the Elemental will stay on the property after the timed summon
3. Grow friendship with the Elemental and look for "move-in" and "join household" interactions.
In the case @Metior_Ice and I were discussing it would be between a Sim and an Island Elemental. In that case choosing "move-in" is important because that option makes the Elemental a normal household member. The "join household" option moves the Elemental into the household but the Elemental stays in a ghost form (see through).
I hope this helps and others will add their help for you also.