Another expert here - a retired CPA
Here's the problem I don't see addresses in the previous response related to the income tax aspect of your questions:
Can a rental house BE your primary Residence?
Do we NEED to declare one?
Is there a Legal/Tax definition of that and what would be the benefit?
Could we just say we are renting and not have a Primary Residence at all? (we plan to travel a lot...)
First of all, yes, a rental house may be a primary residence, but that only relates to 1/2 of the property and has no tax implications for you.
Since your wife & your sister-in-law own the property, here's how it will work for tax purposes:
Once you move into the house that your wife owns 1/2 of, that 1/2 will be considered your primary residence from an ownership standpoint. The other 1/2 will be your sister-in-laws rental property, as well as your rented 1/2 primary residence.
How you determine that you are going to split the expenses is determined based upon the ownership interests.
For example, if you pay 100% of the expenses of the property since you are living in it, 1/2 of the expenses would be deemed to relate to your primary residence and to the extent deductible (for example the real estate taxes) 1/2 of what you pay would be deductible on Schedule A & the other 1/2 should be paid by your sister-in-law and be considered by her as part of the rent that you pay her.
Most of the rest of the expenses, that you pay 100% of, would not be deductible for income tax purposes for your primary residence, say for homeowner's insurance, utilities, maintenance, landscaping, etc.
So, from a tax standpoint, the best way for both of you to handle that is for you to pay 1/2 of most of the expenses as relating to your primary residence & the other half should be paid via your rent to your sister-in-law who can then pay her 1/2 and deduct them against the rental income you pay her for her 1/2 of the property.
If and when it comes time to sell the property, 1/2 will be deemed as your principal residence and as long as you meet the requirement of living in the property as your principal residence for any 2 out of the previous 5 years ending on the date of sale, you will be able to exclude up to $500,000 of capital gain on your wife's 1/2 of the property as long as she files a joint return with you for the year of sale.
Your sister-in-law will report her 1/2 of the proceeds as a sale of rental property and be taxed accordingly.
In your case, based upon a previous comment you made, the time that you travel away from the property, will count as occupying the property as long as you don't establish a permanent residence somewhere else.
Let me know if you have any follow-up questions.