I am aware of the many sources that discuss the reasons a woman should or should not light, and rather her husband should be Motzei her.
If my wife does choose to light her own Chanukah candles, does she make her own Beracha?
If the answer is, that my beracha is for my whole ״בית״ and therefore she should not light. Then why do all aged children make their own beracha, they should be included in their fathers beracha on the ״בית״ ?
From the wording of your question “if my wife chooses” you are inferring that your wife is the one to decide the halacha, and the minhag in Klal Yisroel!
Even if she “chooses” not to according to the poskim and the minhag, she should still listen to the bracha from her husband, and answer amen. She is different that the children who make the bracha by themselves because they are doing like mehadrin min hamehadrin, which includes the making their own bracha. On the other hand, a married woman is not included in mehadrin min hamehadrin, this is because a man and his wife are considered one body and have only one obligation. Therefore since the husband already lit it is as if she also already lit, and therefore if she would make a bracha it would be a bracha l’vatala. Even if there are sources that she may light, she would still not make a bracha because safek brachos l’hakel.
By the way, the gemora says “gadol h’oneh aneim yoser min hamivarech”, the person who answers amen gets more reward then the person who actually made the bracha, one of the reasons for this is because amen has the gematria of 91 which is the gematria of the name A-D-N-Y, and the name Y-H- V- H. The person making the bracha is only blessing H-shem with the name A-D–N-Y. Therefore the person answering amen is considered to have blessed H-shem on a higher level, ( although they don’t have a speaking part). Therefore she is not losing out by answering amen to her husband’s bracha, and this is the way that H-shem wants her to fulfill the mitzvah of lighting chanukah candles.
Have a happy Chanukah
Maharshal siman 85, Eliyahu Rabba 671-3, Pri Migadim ibid M:B 1, Shar Hatzion ibid 10, Kovetz Halachos 11-9.