Can a married woman convert to Islam even if her husband does not convert or even have interest in God?

no problem at all and you will be welcomed in the muslim community but it is important to inform your husband of that and to try to convince him to convert too although i know that they are stubborn and about rearing your children there will be no problem at all and god will be beside you do not worry i can estimate your feeling now about doing such step but fear to be accepted has no bases or clues