The Lingam is the form of shiva. The avudai or Peeta is Vishnu and The padma thala or the lotus part below as base is brahma. I think nowhere shakthi is depicted here. Anyhow shakthi and shiva are inseperable (like the flower and nectar, like the lamp and its hotness). It is very well one can do abhsikeam and aradhana to shakthi without shiva (As the form is filled with vatsalya and karuna). Whereas doing the vice-versa I think is not acceptable.
The aunty might not think that you have not invited and she will be ready to come for the function. Whereas will the uncle allow it? He will says that you have not been invited. Why unnecessary you also comes there and waste your time and energy... Also will it be right to invite only one when both are there in the house??? So Gopalan sir is right.
At the sametime, you can perform poojas to shakti alone thinking her as your child, treating her in the same way. So there is no need of shiva there. Anyhow worshipping both of them together will be the good thing.
Pranams