And OP you can ignore this stereotype. Thais are individuals. As in any country, some manage their money well and some don't; nothing so far suggests she doesn't. And why shouldn't she look on a dating site for a partner? A government employee stuck in office won't find it easy to meet a new partner, esp. a foreigner. Most members here seemingly know only uneducated lower class Thais, and many of those women used to work in bars or massage parlors.
As said a few times already, just take it slow and easy, get to know the lady, the kids, the extended family before making any commitments--and also before hopping into the sack. Her playing the sex card early would be a warning sign. Keep your options open. Re: the kids, they could be wonderful and add a lot of meaning and purpose to your life. Or they could be horrors. :)