Sounds like you have recurrent Graves Hyperthyroidism despite 2 doses (important to get the exact I-131 doses so if a third dose is given, it will be high enough).
Now with pregnancy, things are more complicated. I usually would use PTU (an anti-thyroid pill) in this setting to control things during pregnancy and nursing, then treat with I-131 (29.9mCi) -- a month is a long time to be away from the baby, a week or two is more reasonable, but certainly cannot nurse after I-131 and must be done with nursing for at least 8 weeks before I-131 (as I-131 can accumulate in breast milk and cause breast radiation damage).
Surgery is another option that avoids the I-131 and radiation safety issues. Still would use PTU during pregnancy to keep levels in high-normal range then surgery about 6 weeks after delivery. Recovery is about a week.
Synthroid is fine (and very important) during future pregnancies.
The most painful time is the hours after surgery until about 24 hours. You will receive mdication so it should not be an issue. I know of many people including myself that began taking Motrin after the first 48 hours.
Picking up your child may be restricted for up to 2 weeks while your incision heals depending on how much they weigh when you have your surgery.
Synthroid is a synthetic hormone replacement and will not cause issue getting pregnant if your levels are in normal ranges.
Please be sure and research your surgeon's experience level thouroughly. Someone who performs 3-4 thyroid removal's per week is highly skilled in most cases. Many surgeons are now performing minimally invasive technique which leaves a scar of only 3/4 inch, internal stiches and gluing the incision shut withut drains.