The hill is on my parcel so no issue there, but the problem with using wifi is a weather radio won't alarm based on it. The great thing about a weather radio is it will *silently* monitor the WX band for alerts 24 hours a day and sound an alarm if one is detected.
I think there has got to be a better way to do this.
NOAA used to send out an alert tone that would trigger older receivers. It's not hard to trick a commercial radio with 2 tone paging capability into recognizing that tone and opening the audio for a set period of time. Then all you'd have to do is feed the audio via IP connection down to your house.
Wind could be a problem. This area gets unbelievably strong wind gusts. Are yagi antennas a bad choice in an environment like that? There's an advisory in place right now for 45mph gusts.
A good quality commercial antenna will not have a problem with 45mph gusts. That antenna I linked to is rated for 100mph winds. You'd need to make sure your support structure would handle that, and if you are in a location that gets ice, the additional wind load from ice loading was addressed.
How many dB do I need from the signal on the hill?
The more the better.
The signal strength at the hill top will be boosted a bit by the Yagi antenna gain. The ones I linked to have 9.2dB of gain. You'll lose a tiny bit of that power in the coaxial cable between the antenna pointed at NOAA and the antenna pointed at the house. The antenna pointed at your house will take the signal from the coax and focus it towards your home.
Then there's path losses, that's the normal unavoidable degradation of the RF signal as it passes through the air. For the distances you are talking about, it's going to be in the 70dB range, which means what little signal you get out of the antenna pointed at your house is going to be extremely weak by the time it gets there.
Then you have the gain of the antenna on your roof, again, 9.2dB of gain that will offset a bit of the free space loss.
Then you have losses in the coax going down to your radio.
It's going to be hard to calculate all this without the right test gear, even then there's going to be some slop in the numbers. Add in poor receivers on most consumer electronics, and you'll likely have issues.
You could add a small preamp on the radio end, but that's going to add to costs and noise levels.
If this was an easy fix, more people would be doing it. It can be done, but it's not cheap or easy. I still think you need to look at a more reliable solution.