JMO, but I think that recent history effectively counters your belief that there is a correlation between interest rates and property prices. The last great property market was from 1976-1979. From January 1976 to January 1980, the fed funds rate rose from 4.87 to 13.82 percent. During that time real estate values skyrocketed. In his 1981 book Wealth and Poverty, George Guilder notes that by 1979, the value of individually owned dwellings had reached $1.3 trillion dollars, twice the worth of individually owned corporate stock. He also noted that half of the newly minted multimillionaires in 1978 achieved their fortunes in real estate.
Conversely, each of the three property bear markets during the last 30 years or so (1974-75, 1980-82, 1990-92) occurred while rates were falling. Real estate is the most frothy when the dollar is weak. To state that housing prices must go down because interest rates are rising ignores recent history.
Maybe there is a connection and the effect is the other way around; namely that increasing real estate values drive up interest rates.
The reason I'm suggesting this is the fact that if you squint real hard at the long term trends you can almost see interest rate surges happening right after big increases in real estate values.
Just the same, I try to take this stuff with a grain of salt because one problem is that the human brain has a bad habit of seeing patterns even when there are none, and another problem is that even if there were a connection it's definitely not strong enough be able to predict anything.
It does look like something though...