Welcome to HCM,
I can understand she was operated for Thyroid
3 year back and now she is taking Thyroxine
and dose 200 micro gram /day was high as her T 4 was 14 hence dose is reduced and after reduction of dose . I am sure she must be feeling better.
Please be in touch of your Physician to adjust or fine tune the dose of Thyroxine so as to keep you Euthyroid.
can be due to thyroid problem but there are many other causes for infertility,both should visit a Infertility specialist and get investigated and treated accordingly.
There are many options please do not worry.