Disability Benefits: Would Buying Home with a Parent Affect Social Security Benefits

I'm currently on SSI and SSDI disability and own my home. My Dad also owns his own home. We have been thinking of selling both of our homes and combining our money from the sales to get a better home together. A house we found seems perfect for us. It has the main house level, and then it has a lower level that accessible by simply walking down a flight of stairs. The lower level has its own kitchen, living room, full bathroom and bedroom. So, we were thinking that my Dad would live upstairs and I would live downstairs, and that way we would sort of still have our independence, although we'd still spend time together.

Now, I have to consider how this arrangement might affect my benefits. My Dad told me of someone else who is on SSI and lives in a similar situation with her parents, and said she had to do it that way in order to not have her benefits affected. I'm not sure of the particulars of her situation though. The house my Dad and I are considering is a single house, and not a house with a rental unit attached with a separate address. So in the eyes of the government, we'd be living together.

Also of importance, the house is around $200,000. The sale of my Dad's current house would be able to fund about 2/3 of the new house, and mine would fund 1/3. We were going to put both our names on the title, with mine being for 1/3 of ownership, so I'd be paying 1/3 of the property taxes, insurance, and utilities.

Here's what I found so far by doing my own research: http://ift.tt/2w4xnGx

The third item down addresses what happens if someone is "helping me pay my shelter costs". But does this apply to our situation?

Disability Benefits: Would Buying Home with a Parent Affect Social Security Benefits