UCC, as far as I know, is just a Microsoft-ism for a certificate with multiple domain names. Let’s Encrypt certificates can have upto 100 names, so it checks that box as well.
In order to generate wildcard certificates (and renew them automatically), you will need to use DNS validation. This means you will need to select a Let’s Encrypt/ACME client that supports DNS validation, and your domains will need to use a DNS hosting provider that is supported by them.
Who is the DNS hosting provider for your two domains? Or do you run your own nameservers, and if so, what is the nameserver software you use?
You will get the intermediate with your certificate, but there is typically no need to get the root certificate as well - it is automatically determined by clients who connect. For what purpose do you need it? Which server software will you use this certificate with?