With CafePress Premium Shop ($5 to $7/month) you would be able to design your shop to match your website, so even if it's cafepress.com/yourshop, your site visitor may not even know he/she left your site, but I understand if that's not what you want.
I am not 100% about the dropshipping details, but from what I understand, you collect payment and orders, you transfer the order to the dropshipper, who then ships the product to your customer. What I am not sure about, though, is whether your dropshipper would charge you upfront or per order. I would think you would need to pay them upfront (and then you would get your money back + profit from your customers), but I could be wrong... but this is something to look into, as I am sure different dropshippers have different methods of doing this.
There are many t-shirt printing companies that would put your design on your shirts and ship them to your dropshipper. I would assume, then, that you would have to place a bulk order (and different t-shirt sizes, etc). So if you have multiple designs and you want different colors, it may add up.
You
CAN do all this, but I just wanted to let you know about the upfront costs, so you're not surprised.
I am sorry if you already knew all this... I am just thinking out loud
