Yes, define two relationships. Your notification have only one "sender_user" right?
So this is the relationship "schema":
1st: relationship Many to Many
- User belongsToMany Notification (A user has many received notifications) [received_notifications]
- Notification belongsToMany User (A notification has many recipient) [recipients]
I suggest naming the pivot table as notification_recipient_users and manually set the pivot table name on relationship, instead of the conventional naming, since your relation isn't so simple.
2nd: relationship One to Many
- Notification belongsTo User (A notification has a sender) [sender]
- User hasMany Notification (A user has many sent notifications) [sent_notifications]
I suggest naming your foreign key on notification as sender_user_id.
Since you have two relations with different meanings, you should call they on a suggestive name, as I suggested on square brackets.