According to MOM, here are the requirements to apply for a LTVP:
1. Hold an Employment Pass or S Pass.
2. Earn a minimum fixed monthly salary of $6,000. This is based on your salary, and not based on your combined household income.
3. Are sponsored by an established, Singapore-registered company (usually your employer).
Based on what you mentioned, you can proceed with the LTVP application for your mother.
For more information, you can contact us at https://wa.me/6584833084