Website Extremely Slow every alternate Monday for 30 minutes

That would coincide with the start of the working week for the eastern seaboard states. What's the function of the website that's hosted on the EC2 and is it something a lot of users might be expected to hit at the start of of the week?

Check the Monitoring tab for the instance in AWS Console, is there any resource usage, for example CPU, that looks like a cause for concern?

To capture more extensive metrics you'll need to setup CloudWatch agent to collect https://docs.aws.amazon.com/AmazonCloudWatch/latest/monitoring/Install-CloudWatch-Agent.html

If this is a regular thing you may want to consider adding the EC2 to an auto-scaling group, and then use scheduled scaling to (for instance) scale out at 6am CT and in at 8am CT https://docs.aws.amazon.com/autoscaling/ec2/userguide/ec2-auto-scaling-scheduled-scaling.html