It's not fantastic news I'm afraid.
She cannot extend her visitor's visa here.
She could only apply for settlement here (rather than from back in Thailand) if there are exceptional circumstances which warrant the UKBA exercising their discretion and allowing the application. These exceptional circumstances would be something of the order that she was required here to look after you and the children because you were receiving serious medical treatment.
I note that you state it has taken you time to get back on your feet so I assume that you taking care of your children is not a physical impossibility (although plainly not a best case scenario because of your wife's potential absence).This would probably not in the view of the UKBA fulfill the criteria of exceptional circumstances. You would have to produce detailed medical evidence supporting your claim that you are physically impeded from caring for your children to such an extent that your wife is required to stay.
If you made an application on this basis then your wife will be permitted to stay until the reach a decision, but if your claim is not well supported by evidence (and you do not have much time to gather that evidence) then it will be a quick decision for them and you will have spent money on the application only to be told that she must return to Thailand.
I would advise you to see an immigration solicitor in your area to pre-prepare your wife's application from Thailand. If the application is well prepared then you can make it easier for the UKBA to reach a decision and this may (may) result them making a decision quicker. As you and your wife have been married for 4 years she can apply from Thailand for indefinite leave to remain straight away and make sure you ask the solicitor that.
I know this is not what you want to hear but unless those exceptional circumstances described above apply and you can adequately prove them by documentary evidence in your application (which you would have to submit before your wife's visa expires) a return to Thailand is the only option.
Sorry it could not be better news.
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