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 is His slave and Messenger.
First of all, all perfect praise be to Allaah, Who guided you to Islam and we ask Him to make you firm and steadfast on His Religion until the day you meet Him.
We advise you to seek beneficial knowledge, perform good deeds and befriend righteous and pious women.
If you refer – in your question – to the visit of your mother’s boyfriend along with your mother to your home, then you should primarily prevent him unless there is a religious benefit, like calling them to Islam and the like, and provided there is no temptation in his presence when you call him to Islam.
If we presume that he enters your home, then you are obliged to fully observe Hijab in his presence because he is not a Mahram to you.
For more benefit, please refer to Fataawa 83033 and 90940.
As regards the will of a non-Muslim, it is permissible for a Muslim to take it; for more benefit, please refer to Fatwa 96163.
Finally, we advise you to be kind and dutiful to your mother. The way of being dutiful to her is to invite her to Islam and make every effort so that she embraces Islam.
For more benefit, please refer to Fatwa 86378.