I'm probably misunderstanding this a bit. But I have a few doubts as to what you are proposing.
Legally, you can either own the whole of the property jointly (in unequal shares) with your parents, or you can split the titles with you owning one apartment and your parents owning the other. Do you understand the implications of each approach, and which are you going to agree with your parents?
You are moving to a smaller house which has two apartments, and are proposing to live in both apartments at the same time. How will this work in practice? Are you planning to keep the two apartments physically separate with separate locks on separate front doors, in which case how does one family manage that? If you are joining the two together, you have a single family house not two apartments, in which case there are potentially zoning and property tax implications.
What are the potential timescales for your parents moving in? What if they decided they wanted to move in only a few months after you do, would you be happy with that? Are you proposing to pay your parents rent while you occupy their share of the property? Who is to be responsible for repairs, insurance and taxes on your parent's share? Is there going to be a formal contractual relationship between you and your parents which deals with all these issues?
Why are you proposing to occupy your parent's share of the property until they move in? If it is because you need the space in order to live comfortably in this smaller house, how are you going to manage when your parents want the space for themselves? If you do not need the space, why will you be using it in the meantime?
Might it be simpler for you to buy the whole house subject to an agreement to rent the apartment to your parents for a nominal amount?
You and your parents may need to sit down with a real estate lawyer to consider the options. I'd add in that if you have siblings who might have an interest in the inheritance of your parent's estate, it might be a good idea to get them on board as well. Otherwise, if your parents have a financial interest in your home and when they die there are questions about how the estate is left, you could be in a sticky situation.
I don't think any of this is insuperable. You are doing the right thing by looking at all the potential issues before going ahead.