Pre-tax contributions to the 457(b) are already subtracted by the employer to come up with the amount that the employer reports in box 1 of the W-2. These contributions are not to be subtracted a second time when determining the amount of compensation available to support IRA contributions. The amount of wages shown on a W-2 that are able to support an IRA contribution are the amount in box 1 minus any amount in box 11.
If your wife earned $43k but deferred $30k to the traditional account in the 401(k) the employer would report only $13k in box 1 of the W-2. Assuming that you have no compensation yourself and you file a joint tax return, that would mean that the IRA contributions by you and your wife combined will not be permitted to exceed $13k.
On the other hand, if your wife earned $73k and deferred $30k to the traditional account in the 457(b), that would result in $43k being reported in box 1 of the W-2 and would be plenty to support your wife's $8k IRA contribution and your spousal $8k IRA contribution combined.
