Outline
According to this website the average latency between eu-west-2 and us-west-2 is around 190ms. That's a lot of latency. US-east-1 has around 95ms of latency, so significantly less.
Most applications are likely designed assuming the database and application server are located closely together. In this scenario the application can make frequent requests to the database without any significant impact to the application. High latency breaks that very reasonable assumption made by developers.
Best Solution - Colocate / CDN
The easiest and probably best solution is going to be to put the database and web server closer together. I suggest putting both in the same region, ideally the same AZ. Use the CloudFront CDN to increase performance by caching most resources close to the user.
This is most likely to meet you compliance requirements.
Solution Two - Read Replica
You can put an RDS read replica in the USA. Change your application so reads go to the local database and writes go to the master database.
This may not meet you compliance requirements.
Solution Three - Database Replication
You could potentially run your database so there are two live, master databases that synchronise with each other constantly. This increases your risk somewhat, and you may have to cater for this in your application, or at least detect it.
This may not meet you compliance requirements.