Postpartum Menstrual Cup/Disc and an IUD

So I've been using Diva Cups for approximately five years. I think I replaced my first one after three years of use but I'm not entirely sure. Aside from a little night time leaking early in each period I've not had a single complaint and have loved the practicality of a menstrual cup.

After the birth of my baby, I had a copper IUD placed and I'm still waiting the return of my period. Since I hate pads and tampons, I was hoping to continue using a menstrual cup but was curious if it could interfere with the IUD or potentially cause expulsion. I've read a few articles but I don't necessarily trust the ones from menstrual cup manufacturers to be unbiased, so I was hoping to hear other women's experiences.

Did a menstrual cup seem to interfere with your IUD?

How about a menstrual disc?

Additional, did you find you needed a bigger menstrual cup postpartum?

Thank you for your responses!