How do you define a "granny house"?

It’s actually referred to as a Granny Flat, not house. And most places require them to be on the same lot that your home is on. They cannot be on a separate lot.

A talk with your zoning department. If the lot is part of your own lot that makes a difference too.

Figuring out what the heck a "granny flat" or "granny house" is would be the first step for me.

Once you figure out if building a granny flat is allowable on your next door lot or not I would do some programming - not the computer type but the architectural version. Sit down with your granny and develop a list of her requirements, needs and desires in the design. This would be things like does she need an accessible bathroom. Should the kitchen be designed for someone who might (or might in the future) have more limited mobility? There are a whole list of things to think about before you tackle an actual design.

As others have posted, the first step is to find out what zoning requirements are.

In most places, "granny flats" are small houses that are built on the same lot. Zoning laws in many places allow them even though technically they are multi-residential in a neighborhood zoned for single family or the total square footprint exceeds what is permitted on a specific lot. Now they are being permitted in some dense areas like Los Angeles as a way of increasing the supply of affordable rental units. .

If the second lot is zoned for another home, why would you want to limit the house built there to the kind of small house that is built as a second home on one lot? It would not be appreciably more expensive to build a more standard home in accordance with zoning laws that are applicable and you would have significantly more flexibility in terms of what you do with the home. A "granny" or mother in law can live in a larger home but generally a family would want a more standard size home - e.g. 3 bedrooms/2 bathrooms.

Don't take this the wrong way, but think about resale in your planning. I am currently designing a home for a client that is 92 years old; we are very frank and open about how the home should be designed for present and future needs.

In a single family district it would be called an accessory apartment where I live and it would be restricted in size and could not be separately owned. It could be inside your house or detached.

The local zoning ordinance should be online. You could google it.

Its wise to learn as much as you can before talking to a building official.