If your wife has a Thai ID card she must have a previous family address.
If it is really important for you both and all connections and family ties are lost my remendation would be that you both come Thailand to where her Thai ID card was issued and get what she needs and treat it as a holiday.
My wife is 54 and has never had a birth certificate but the local province govt officies will supply if she needed one.
A police report to say my wife has no criminal record could also be received from the province head police office.