I had 3 miscarriages & the (elderly) doctor in a very small town said it could be anything: old eggs, bad eggs, etc. We then moved with our job, & the new doctor in California said, have you ever had your thyroid tested? I said "no". That can cause miscarriages, he said. Guess what.....my thyroid didnt work.
What are the reference ranges for the Free T3 and Free T4? Reference ranges vary lab to lab and have to come from your wife's own lab report.
Her Free T3 and Free T4 levels are very low and it will take a while for the medication to bring them back up to a level that's good for her. It takes 4-6 weeks for the medication to reach full potential in her blood, then it will take time for her to get well.
Her TPOab indicates that she has Hashimoto's Thyroiditis, which is an autoimmune thyroid disease in which the body sees the thyroid as foreign and produces antibodies to destroy it. Your wife will have to be on medication for the rest of her life, because her thyroid can't produce the hormones she needs to live, but the medication will provide them for her.
Too low thyroid hormones will cause miscarriage. Thyroid hormones are also necessary for a fetus to grow and develop normally, so it's not good for your wife to get pregnant again until her thyroid hormone levels have come up to a point high enough to sustain, both herself and a baby.
For herself, her FT4 should be about the middle of its range and her FT3 should be in the upper half to upper third of its range. Levels may need to be higher during pregnancy.