Ženatý and vdaná.. is it common in Czech to have two different words for the same adjective between masculine and feminine?
Well, the point is it is not considered the same adjective, isn't it? But adjectives where other languages use one and Czech distinguishes the genders - no, it is not common.
Your sentence would be quite unusual in English, rather unlikely.
First, your previous conversation would have had to establish that there was more than one brother and that one of them was married.
Second, it would have to be clear from the context of your conversation how it is that you "have" this particular married person.
For example: "I have a sister, a bachelor brother, and a married brother. Next week my sister is staying with me, and the week after that I have the married brother."
Czech uses grammatical cases and the direct object here must be in the accusative case.
No, do not introduce unnecessary subclauses where there is none in the original.