I manage a website for a brick and mortar store. A few of the products they can ship. Some things arent cost effective to ship. The current site has a link on every page to the products that are available online. Should I split these 2 websites into 2 domains to build a stronger online presence?
If there are only a few products that you can actually sell online it makes no sense to divide up what little online SE weight you've earned. That being said, you should make sure you've done your due diligence and SEO'd the site to maximize your efforts and make sure you're not undermining them by easy-to-fix mistakes.
I'll add . . . it may be an isolated case, maybe not . . . having the B & M directly associated with the ecommerce store lends credibility, people like to know the site represents real people and real businesses instead of anonymous entities out in the ether.
Another advantage is that you can offer click and collect. Travelling to a B&M store and finding that they don't have quite what you want is a pain but so is taking a day off work only to have the carrier not turn up with the delivery. Click and collect is always my preferred solution for a bulky high value item.