Hey Chris -- welcome to G2G
That's not nearly as stupid as it may seem; wireless signals can be affected by many devices (phones, baby monitors, etc.) so it would not be unreasonable to assume that your alarm may also be affecting your signal.
There's really only two things you can do; one is to change the channel on which your router broadcasts and the other is to buy new hardware which uses different frequencies. Since changing the channel doesn't cost any money and is a simple thing to do, we'll focus on that.
Basically, you need to login to your router's web interface, navigate to the Wireless section and look for a "Wireless Broadcast Channel" or "Broadcast" or "Wireless Channel" or any similarly-named property (it varies from manufacturer to manufacturer). Once you have found that, change the channel to a different channel. Channels 1, 6 and 11 would be good channels to test on. Simply change the channel and then test if the issue still occurs. If it does, try a different channel.
If you do not know how to login to your router's web interface, please post the make and model and we will attempt to walk you through it.
- Dan