Should the husband agree to his wife's seeking another shaykh, or should he be satisfied with the previous fatwa regarding the non-occurrence of divorce in a state of extreme anger?

Whoever seeks a fatwa from someone whose knowledge and piety they trust, may act upon that fatwa, and is not obligated to consult anyone else.

So, if you asked people of knowledge and they gave you a fatwa that satisfies your conscience, you are not obliged to ask another mufti.

As for your wife, if she is not reassured by that fatwa, she is not obliged to act upon it. Rather, she must ask until she is reassured, and it is not permissible for her to act upon something she believes to be invalid. You do not have the right to compel her to do so. The solution is for her to go to another mufti.