She suffers from bipolar disorder and asked her husband for khula‘

Praise be to Allah.

Merely taking the wealth and saying okay does not count as khula‘; rather what appears to be the case, based on what people do in such situations and given the fact of the wife’s illness, is that the husband is taking the wealth from her and pretending to agree with her so that she will calm down and this psychotic episode will pass, and this is in fact what happens. So long as the husband does not remember what his intention was at that time, the marriage is deemed to still be in effect and no khula‘ has taken place, because divorce (talaaq) cannot take place when there is uncertainty, unless the husband is certain. 

Ibn Qudaamah (may Allah have mercy on him) said: If a man is uncertain as to whether he has issued a talaaq, the rulings thereon do not apply to him. This was stated by Ahmad and is also the view of Abu Haneefah and ash-Shaafa‘i. That is because the marriage contract is proven for certain, and cannot be dissolved on the basis of uncertainty.

End quote from al-Mughni (10/514) 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Uncertainty in the case of talaaq does not count for anything, because the basic principle is that the marriage remains valid. 

Some of the scholars said that piety dictates that the talaaq should be counted as such, even if there is uncertainty about it. Others said that piety dictates that talaaq should not be counted as such when there is uncertainty, and this is the correct view, because the basic principle is that the marriage remains valid. So piety dictates that one should affirm the marriage. Moreover, if we were to say that piety dictates that the talaaq should be counted as such, we would be doing two things that are contrary to Islamic teaching: (i) separating husband and wife and (ii) – which is worse – making this woman permissible for someone other than her husband, because she may still be married to him. Moreover, if you say that piety dictates that the talaaq should be counted as such, what that means is that you are going to deprive your wife of maintenance, of inheritance if you die, and of many of her other rights.

End quote from ash-Sharh al-Mumti‘ (13/170-171) 

To sum up: your marriage remains valid and no khula‘ has occurred. 

We ask Allah, may He be exalted, to heal you and set your affairs straight. 

And Allah knows best.