All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Undeniably, your step-mother’s brothers are not among your Mahram men; accordingly, the due Islamic ruling regarding Mahrams does not apply to your relationship with them and this means that it is impermissible for you to stay in seclusion with any of them, expose your ‘Awrah before them, and the like of the due and known rulings in this regard. Furthermore, your step-mother, who has done a great job bringing you up, should understand and accept this fact. She should bear in mind that Muslims should comply with the Islamic Sharee‘ah and should not violate the due Commands of Allaah The Almighty. Allaah The Exalted Says (what means): {It is not for a believing man or a believing woman, when Allaah and His Messenger have decided a matter, that they should [thereafter] have any choice about their affair. And whoever disobeys Allaah and His Messenger has certainly strayed into clear error.} [Quran 33:36] Moreover, Allaah The Exalted also Says (what means): {The only statement of the [true] believers when they are called to Allaah and His Messenger to judge between them is that they say, “We hear and we obey.” And those are the successful.} [Quran 24:51]
Additionally, we believe that if your step-mother knew the Islamic ruling on this issue and that it is impermissible for you to meet her brothers unveiled, she would not object to it, instead she would encourage and help you to adhere to your Hijab duly before them. You can show her this Fatwa so as to convince her. However, the above mentioned ruling applies only if you did not suckle from your step-mother five attested breast-feeds (minimal number of breast-feeds necessary to establish the suckling-kinship) in the first two years of your life. If you have, then she is considered your suckling mother, and her brothers are your suckling maternal uncles.
Allaah Knows best.