How to sing slow songs better?

The best solution is indeed to contact your vocal teacher and ask about this, it is most likely that you are not supporting your voice by keeping your diaphragm activated when singing. This is far too complicated to learn on one's own though, because if you do it wrong, it is very likely that you could damage your throat and get hoarseness and/or vocal nodules. So, please wait until the family things are settling down and then ask your teacher when you next have a lesson.