Lao - have you fully researched giving up US citizenship? You have to continue to file taxes for 5 years after renouncing and you basically be blacklisted from ever returning to live in the US. It really only works for the extremely wealthy.
Do you really make enough money as a pilot/stay at home mom (just guessing as you said you have been indoors with your kid all week) to justify this? As in significantly more than the $100K that's tax free for overseas residents plus the deductions for housing and living expenses?
I wouldn't plan where to live based on renunciation alone, if that's the appeal of Singapore. There are other considerations. Your daughter may wish to go work or study in the US one day and giving up your citizenship will make that more challenging. Our real estate agent in HK studied in the US and was not able to get a work visa to stay, she is still upset about it...