Help needed on E Commerce Platform choice based on Database integration

I am a web developer for an employer who is a 35 year old existing door to door sales company with a large sql database. We are looking at expanding our business by using an ecommerce platform. We have done some trials and looked at Volusion, Magento etc., the issue is we would like something that would allow us to have access to the database so we could integrate it into our main SQL database inhouse. Volusion had a proprietary database. I am aware we would need to setup an API or something to facilitate the data transfer from our ecommerce database to our main inhouse SQL database, but what platform would allow for easiest integration? Is these possible or are we looking at a complete custom shop?