Going to his second wife, who lives with his mother, on a day that is not hers
It is permissible for the husband to go to his second wife during the day if that is for a reason, such as checking on her, or giving her her maintenance or taking something from the house and so on.
He may also be intimate with her however he wishes, without having intercourse, but he does not have the right to spend a lot of time with her.
But if that is at night, then it is not permissible for him to go to her unless it is necessary, such as if she is very ill, or there is a fire and so on.
This has been discussed in the answer to question no. 106513.
But it seems that you are going there to visit your sick mother, and asking about her is permissible by night or by day, so long as your intention is to visit your mother, and not to visit your wife.
In this case your visits should only be as long as necessary, and when you have achieved your purpose of checking on your mother, taking care of her, helping her with what she needs and comforting her, then you should leave and go to your other wife, and you should not stay with your mother for a long time when there is no need for that.
And Allaah knows best.