You do not amend a tax return for a mistake you made on the W-4 you gave to your employer.  You just need to complete another W-4 and give it to your employer.

Go to this IRS website for the tax withholding estimator - https://www.irs.gov/individuals/tax-withholding-estimator

You will need to complete a Kansas K-4 to give to your Kansas employer - https://www.ksrevenue.gov/pdf/k-4.pdf

When filing your state tax returns you need to complete a nonresident Kansas return and a resident Missouri return.  Complete the Kansas return before the Missouri return to that you can enter on the Missouri return tax credits for payment of Kansas income taxes.

Amending your tax return will not help you with the fact that you did not have enough tax withheld from your paychecks. during 2022.   You cannot go back in time and change the amount of withholding for the previous tax year.  All you can do now if you have not been having enough withheld is pay what you owe and change the amount you are having withheld going forward.

https://www.irs.gov/individuals/tax-withholding-estimator

https://www.irs.gov/pub/irs-pdf/fw4.pdf

And...since you live in one state and work in another state, you file a non-resident state return for the state you WORK in first, then prepare a return for the state you live in.   

https://ttlc.intuit.com/questions/2895920-why-would-i-have-to-file-a-nonresident-state-return

 If you have federal tax due you can pay by mailing your payment with the 1040V voucher, (which has the address printed on it, having the payment taken out of a designated bank account, or you can pay directly on the IRS website. 

https://www.irs.gov/payments

https://ttlc.intuit.com/community/tax-payments/help/how-can-i-pay-my-federal-taxes/00/26212

https://ttlc.intuit.com/community/tax-payments/help/how-do-i-pay-my-irs-tax-due-with-a-check-or-money-order/00/26403 

To apply for a payment plan with the IRS

Apply Online for a Payment Plan

You must pay your state tax due using the state’s preferred method of receiving payment.  For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.

https://ttlc.intuit.com/questions/1900884-what-are-my-options-for-getting-my-state-refund-or-for-paying-any-state-taxes-i-owe

https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue

A W-4 is simply the way provided by the IRS for workers to estimate their income tax so the employer will withhold an amount that is close to the tax you owe.  Your actual tax is only calculated on your tax return.  If you owe more than was withheld, you must make a payment, and you may be subjected to penalties for being under-withheld during the year, even if you pay in full when you file.

You and your spouse should prepare new W-4s at both your jobs.  Get one copy of the W-4, fill out all the worksheets  (all 4 pages, not just the front page) and use the result to prepare both W-4s. 

You can also use the IRS calculator here.

https://www.irs.gov/individuals/tax-withholding-estimator