I have to use two domain names mywebsite1.com and mywebsite2.com to host the same S3 website. I own both the domains and I have programmed the mywebsite2.com to redirect the traffic to mywebsite1.com but that changes the URL to mywebsite1.com which I do not want. Any suggestions will be appreciated.
You can use two domains for pointing to the same S3 website by leveraging following services of AWS - S3 , Cloudfront and Certificate manager.
You can refer to the following article which explains the complete steps for achieving it.