When I test a client's website in dnschecker.org it shows 3 IP addresses. Is this something to do with how amazon hosts websites? Other sites I check have only one.
This answer summarises the comments above, so people don't come in and try to help, as it's not marked answered.
Multiple A Records
Multiple A records is round robin DNS, a type of load balancing. It relies on the client making requests based on round robin, rather than just using the first entry.
Moving away from AWS
To move away from AWS you simply delete your current public records (A / Alias) and put in new A records with the new IP address.
Suggest you export all data from the instances, databases and data, or even do a backup of the instance you can keep outside of AWS. You'll want something like Restic or Macrium reflect, as AWS doesn't make this easy.
Cleaning an AWS Account
Next I suggest you stop your EC2 / RDS instances, but don't terminate them, in case something goes wrong with the new website. After a few days of the new website working you might create a snapshot of your EC2 instances / backup of your RDS instances and delete the instance, as snapshots are cheaper than instances. After a month you may want to delete all resources in AWS, to save the cost. There will probably be resources all over the place - EC2 / RDS snapshots and backups, S3 buckets, lambda functions, etc. Cleaning an AWS account could be tricky, so if it's not required for something else just close the account.