Well you can do almost anything with Rainmeter ! if the data or updated images are available on the web...
I already made one skin for me to have weather alert warning from the Météo Média site, the french version of The Weather Network, (icon and even a sound alert !).
And Rainmeter can also download updated weather images, and show or show it on demand in the skin.
In your case a custom skin have to be made, because you have to parse the data (if it available of course) from different webpages.

Right now I'm using the Azenis 2 theme, in the screenshot I start the simple skin and manually add the weather warning sign (right now I don't have any weather alert !) I also add an image of a prototype weather station skin made in 2006, who got updated images from the internet (moonphase and the cloudcover map) in it.

I always make my Rainmeter skins, unfortunately I never upload them for public download.
And yes, the regexp is a little bit tricky !
If you give me the link of your location weather page, and for the radar image that you want, I can try to parse it, make and send you one default skin, so you will be able to do something with it after...
But for the weather alert, this is possible take of time, because I will have to wait for a weather alert to be able to parse it and test it.

Bad & Good news

Bad news
I can't get the radar image from weather.com, because it embed in a Java feature !

Good news

Well I find that you have a private weather website dedicate for Lawrenceville GA
WWW Link
1- he have a radar map (third-party provider), update rate 20 minutes, and I can download it !
2- he have weather alerts (third-party provider), and I can parse it, after a couple cups of coffee, and a pack of cigarettes lol
3- he have his own private weather station, so update rate for the temperature, humidity, pressure... around 15 minutes !
I did find one website for my city (Montreal, Quebec, Canada) who use the same private weather station, it was a school near my house, but unfortunately they only generate images, no weather data texts.
WWW Link
(I,m beginning to be jealous of your luck !...)

I make a default skin, the parsing code include other weather datas, in case that you want to use them.
Testing it right now, I'm waiting to go back with no alert, just to be sure if my parsing is o.k (dynamics webpage, parameters of the page are changing)
In a short time I will send you a PM with my e-mail address, so you can tell me where to send the skin, and to be able to communicate with me... the skin will work until he decide to change his webpage !

Here a teaser screenshot !

VeuveNoire,

I like your rainmeter Weatherstation very much!!!

I've tried different weather configs, but not one so nice as yours.

Would you please help me to config such a meter?

Thanks in advance!

Greetings,

Kebas.