I realize we are in the first steps of learning the language here, and it can be confusing to introduce and accept every possible nuance of meaning, but is there no situation in which "Mám ráda tvého muže" can be understood as "I like your man"? Consider man in the sense of "We (an army) are looking for a few good men." In this context, if a captain says to his sergeant, "I like your man," how would this translate?
No. When preceded by a possessive pronoun MAN and WOMAN always have a meaning of the person married to the person we are using the pronoun for. "..tvého muže" is in Czech clearly a husband not just a man.
A captain would use different word for MAN than muž. CHLAP for example, or soldier, recruit but he would avoid singular muž. When it comes to plural, he could say muži, though again use of soldiers, people, recruits is likelier. Or "mužstvo" which is more ore less "team"
Of course, there is always some simplification in our explanations. We can rarely write a whole treatise. Of course, when speaking about a military or police squad, "mí muži" are "my men".
However, this is extremely unlikely here. If it were about on of the men in the squad, she would use something like "Mám ráda jednoho z tvých mužů." to avoid confusion because "Mám ráda tvého muže." is so usual and expected for "I love your husband.".
In casual speach "chlap" is indeed likely for the members of any squad but "muž" is likely to be used in official communication.
Another way to avoid the confusion is:
Měl bych zájem o jednoho tvého muže. - I would be interested in one of your men.
Zadržuješ jednoho mého muže. You are holding one of my men.
Máme jednoho tvého muže, zajatého... We have one of your men, captured...
"jeden tvůj muž" nicely avoids "tvůj muž" that is too much like "your husband"
To clarify: I see no reason why a captain (whether it be a sports captain or a military one) shouldn't use "muž" (among other options such as "chlap" or even "kluk" in the right setting) when speaking of his men. What the captain would not do is say "můj muž", but then he would likewise avoid saying "můj chlap" or "můj kluk".
"tvoj" is not a word. It's "tvůj".
Calling someone's partner, who is not a husband, "your man" is unusual even in English. What word you'd use in Czech depends mainly on the level of formality or familiarity with whom you're talking to. For example, "tvůj partner" and "tvůj přítel" are both formal options, "tvůj chlap" is an informal option, "tvůj kluk" can be used if you're talking to a young person to mean "your boyfriend", and "tvůj +name of the guy" is always a possibility, of course.