Troubles trying to run locally with Laravel Homestead

Hi, total newb to OpenCart here, but familiar with programming PHP / MySQL so feel like I should understand any instructions from anyone kind enough to reply.

This is what I'm doing. I have a client site running Version 2.1.0.1 that I'm trying to set up locally to run under laravel homestead, which uses Nginx instead of Apache so .htaccess isn't looked at but requests are routed to index.php. I've downloaded the code and copied it to /mysite/public/shop and set up two different servers pointing at this folder, onlineshop.domain.com and onlineshop.otherdomain.com, and put in hosts entries to make sure those URLs are routed to the web server. I created a database with the proper credentials and *almost* everything seems to be working on onlineshop.domain.com which matches the domain the site was on when it was live. I updated /mysite/public/shop/config.php and /mysite/public/shop/admin/config.php to have the proper paths and database connection strings. My assumption was at this point I should have a fully functioning local copy.

However, what I'm seeing is that the dahsboard on onlinshop.domain.com works nearly perfectly (some UI bugs that I don't know if they're just part of the release) but on the front end none of the URLs work. The URL in the address bar updates but only the content from the home page is displayed.

I added a second store at onlineshop.otherdomain.com but when loading at this URL none of the CSS is loaded. I haven't tried the dashboard for this domain, they should only need the one login to manage both stores.

I'm a little lost as to what to do next as far as troubleshooting or changing configs or whatever. Any advice is greatly appreciated.

Eventually what I'd like to see is basically the same store from both onlineshop.domain.com and otherdomain.com/shop. I plan on using https://opencart-api.com/ to manage store products and shopping carts from a CMS with a ReactJS powered frontend that allows building custom products. It's a little frustrating to be stuck just getting it running locally.

Well, you should better work with something 'DEFAULT', instead of using
a strange Server, not even allowing a bloody .htaccess file to work. It will
force you, to change 'default' OC Code, and so disable you automatically
from beeing able, to make use of 'basic' OC Wisdom and Assistance, since
it surpasses the knowledge of most OC Users and Forum Helpers, as I guess,
and makes you depending on paid professional help.
Good Luck!
Ernie