Sag ihr, dass wir sie lieben.
"Tell her that we love her."
At first when I read this I thought, aha this is formal because of the ihr but then I realized that the ihr was not "You tell her" but simply Tell her. Oder?
"ihr" is a tricky one - at least if my husband is any indication ;-) If it's capitalized, you definitely know it's formal, e.g. "Ist das Ihr Mantel?" If it's not capitalized it can either be "her"(dative) or "you" (plural nominative). If you have to translate the above sentence into English, I think the most common way would be to just say "tell her" although I could also imagine somebody putting extra emphasize in there and saying "You tell her,...". Has that answered your question? Or did I miss something?
You are correct, the sentence means "Tell her that we love her."
There are several grammatical structures at play here.
Sag --> singular informal imperative form of the verb sagen. The imperative is a grammatical mood used for making requests or giving commands.
For reference, the imperative forms of the verb sagen are as follows: singular informal: sag! (in textbooks, imperatives are often given with exclamation points to reinforce the idea that it is a command) plural informal: sagt! singular/plural formal: Sagen Sie!
ihr --> this is a tricky one, because ihr has so many different uses (as a possessive, as the second person plural you, and as the third person singular dative her). In the sentence you gave, it's the dative.
, dass wir sie lieben --> this is a normal indicative subordinating clause, and you translated it correctly.
Therefore, the sentence as a whole means: Say/tell (to) her that we love her. As far as I can think of, this is the only reasonable translation allowed by the German grammar structures used in the sentence.
Hope this helps.