1 You have been a great support to my mom.
This is fine. It sounds like the person has actively supported your mom.
2 You have been a great support of my mom.
This is not quite correct. You can say someone is a supporter of someone or something, but this normally means that they are championing them, or are a 'fan' of them rather than helping them.
3 You have been a great support for my mom.
This is also fine. The difference to option 1 is that this could be taken to mean the person was supportive of your mom when required. When someone is "there for" someone else it means they are willing to be supportive, if needed.