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Can you stop breastfeeding while taking the medications?
You should try Gynera, Minulet, Femoden, Femodene, Katya and Millinette 30/75 which contain 30 μg of ethinylestradiol and 75 μg of gestodene. The clinical study didn't show weight gain compared to placebo. It is okay during lactation. But the bipolar medication could interact with the pills. Your doctor should adjust the dose of the bipolar medications.
The IUD contains the same hormone as the depo shot. The clinical study described complaints of hormonal side effects (including hirsutism, acne, weight change, nausea, headache, mood changes, and breast tenderness) are the most common reasons for elective IUD removal in the first 36 months of use. I think it would cause weigh gain and mood changes.