I personally prioritize putting money in taxable before I would do a non-deductible traditional IRA, so I agree with you there.
You are limited to contributing up to $6K per year total between your Roth IRA and traditional IRA. So you could contribute $5K to a Roth and $1K to a traditional, or $3K to each, or whatever. So if you already maxed out your Roth IRA you can contribute $0 to your traditional because of this combined limit.
That combined limit applies regardless of whether the traditional IRA contribution would be deductible.
Your wife is probably eligible to make a full $6K contribution to either her Roth or her traditional IRA via what's called a spousal IRA contribution. In essence if the two of you make more than $12K and you're married, she can use your earned income to contribute to her IRA.
Whether her traditional IRA is deductible, I'm not sure on that - check the rules at irs.gov. ETA: A quick Googling suggests that if you have a workplace plan but she does not, then as long as you are MFJ and your AGI is under $193K then her contribution to a traditional IRA would be fully deductible (cite:
https://www.investopedia.com/ask/answers/081414/can-i-deduct-my-individual-retirement-account-ira-contribution-my-tax-return.asp).
But again, if your wife maxes out her Roth IRA, she would be ineligible to contribute to her traditional IRA. But that is because of the combined limit noted above and not (necessarily) any other reason.
As
@Telecaster notes, you could possibly do a backdoor Roth as well, but that's a more advanced topic so I'd recommend you solidly understand the basics before trying that.