Hi,
You are correct that the personal allowances would be deducted off gross pay, so the standard personal allowances of £12500 divided by 12 = £1041.66 per month tax free, anything over this is then taxed at the appropriate tax rates.
If your wife is resident in Scotland your wife's income will be subject to the Scottish rates of income tax.
Please find attached a link to guidance which may help.
Income Tax in Scotland
Thank you.