If it's always YOU that send the money, how do you understand the sentence like: 東京の大学に行っている弟に毎月家から十万円送っています? It could be you, but most probably your parents.

The second sentence means that YOU send 100,000yen. The first one means you are the receiver of the money. With "～くる”, the speaker/writer is the one who is done the action. e.g.: ボールを投げてくる　someone throws a ball (to here / to me) 手紙を書いてくる　someone writes a letter (to me) ...

The first message says you are the one receiving the money whereas you are saying in the second somebody, could be you but most probably your parent, is sending money to some other member of your family. Kazuki, thank you for your question and good luck with your Japanese.