I'm confused. Is she looking for a partner for her dad or for her?

Most likely for Tia I think

I was confused too when she says 'Wife' like what? mc is now lesbian now? xD

Translation is a bit off.
The empress is trying to find a marriage partner for Tia. Of course a man who is under their influence. Since Gallahan is fcking rich now and Tia is his only heir, they want to pair Tia with someone on their side so they will have some of Gallahan's money.