Both your options are valid, though I'd seperate the web app from the REST API if you can. It will let you easily upgrade your API separately from your web app and help separate those two concerns.
Along those lines, you could use a Javascript framework like Angular for the web app and have all the apps use the REST API you build in Laravel.
Basically, have all your apps (mobile and web) use the same REST API, however you choose to program them.
Good luck!