Can a muslim woman refuse to go for abitration in order to resolve the problem as the husband wants to reconcile
“And if you fear a breach between the two, appoint an arbiter from his relatives and an arbiter from her relatives. If they both desire reconciliation Allah will affect harmony between them. Verily Allah has full knowledge, and is aware of everything.” (An-Nisa 4:35)
Why would you wish to disobey your Lord?
Trouble within a marriage seldom, if ever, involves just the husband and wife. Even where there are no children there will be parents, and other family members, who could be affected by decisions made by the couple. Where there are children then the affect will be all the greater. I’m sure that you are aware of this.
Note the words of our Lord: ‘If they both desire reconciliation….’ The key word is IF.
A troubled couple do not have to be reconciled; and the process of arbitration cannot force them to. What it can do is smooth the path to divorce (if that is indeed inevitable).
I cannot tell you what to do. I can ask only this: What would you lose by agreeing to this process?
I hope this helps.