My mother comes to stay at our house at least once a month.
Literal
Mother [topic-は] at-least month [per-に] once [topic-は] home [to-に] stay-[purpose-に] come-[benefactive-てくれます]
少なくとも = at least. 月に一度は = 'at least once a month' — は adds emphasis ('at least this much'). 泊まりに来てくれる = 'comes to stay (as a favor to us)' — stacks purpose に + benefactive てくれる.