That court process exists precisely for deadlock like this: one spouse wants to sell and needs the proceeds, the other will not agree, and neither the Homesteads protection nor a refusal is meant to trap someone indefinitely. A judge weighs both sides before ordering a sale, not just the applicant's preference.
Getting there usually means retaining a lawyer, since this runs through the Court of King's Bench rather than a simple listing conversation, and legal fees of $800 to $1,500 for a straightforward sale are a different budget line than the cost of contested litigation.
Before it gets that far, an independent, hand-reviewed number both spouses can look at often removes the disagreement that started the standoff in the first place. Get your hand-reviewed valuation from Joel Dyck.