Yes, you can absolutely do pooja even if your mom is on her period.

In Jain Dharma:

• Menstruation is related to your mother’s body, not yours.
• If you are clean (snan/bath done, clothes clean, mouth clean) and have shuddha bhav (pure thoughts), you can do:

- Navkar Mantra - Chaityavandan - Stavan, bhajan - Samayik, prarthna, dhyan, svadhyay

Some families have customs that:

• A woman on her period avoids dravya-pooja (touching/bathing idol, going in garbhagruh, handling pooja samagri or scriptures) and focuses more on bhav-bhakti (mantra, stavan, dhyan). ( jainknowledge.com)

But these rules apply to her, not to other family members.

So:

• Your mom on her period = you can still do pooja normally.
• Just follow your home/sangh’s maryada if they have any special rules.

If you want to read more on this topic, you can see related Q&A here