You need to explicitly request that every domain and subdomain you will use is included in the certificate. As an example, a certificate for example.com will produce errors if users receive it from the server when browsing for www.example.com. The certificate would need to have both names: example.com and www.example.com.
You might have to ask HostGator about that one Hopefully!!!
Unless something has changed, HostGator is actually one of the worst hosting providers to deal with if trying to use Let's Encrypt. According to this help page on their site, you must open a support ticket for them to install a third-party certificate (like one from Let's Encrypt), and they charge you $10 for this. Since Let's Encrypt certificates have a 90-day validity period you'd end up spending at least $40/year on "certificate installation fees", unless you have a "managed dedicated server" with them. From that page I linked:
The fees to have HostGator install a third-party SSL on your behalf are as follows:
For a single domain SSL the fee is $10
For a multi-domain SSL the fee is $25 for up to 5 domains plus $5 for each additional domain beyond the first 5.
Managed Dedicated Servers can have HostGator install any SSLs free of charge.