You are right, but as in all things the man maths applies.
By paying an amount asked for by HMRC I will get an extra £40 a week at 67. If I continue to live in a little over 2.5 years after my 67th birthday I will have have got that money back. If I live to 95 it will probably be one of the better decisions of my life, if I drop dead in the next 6 months it will almost certainly have been one of the worst.
When I accepted early retirement the max was 30 years, I had 35. I did not expect the rules to change, but they did.
The conflict was that I retired at 51 and have paid nothing since, therefore if I am paid £40 per week short it is something which I can live with.
There is no right or wrong answer here and I certainly don’t feel like I have won anything, but we have to occasionally stick our finger in the air and see which way the wind blows.
Does she have an NI number? If not then I assume she's out of luck (unless she gets one)
If she is then, as you have a child, she can register for Child Benefit, tick "don't pay me the money" and she should get a year of NI credited until your child turns minimum 16 years old
You CAN be paid the money but it is an extra thing to go onto your tax return, even if she gets the money, as YOU earn >£60k/year
From here: https://www.gov.uk/child-benefit
By claiming Child Benefit, you can get:
an allowance paid to you for each child - you’ll usually get it every 4 weeks
National Insurance credits which count towards your State Pension
a National Insurance number for your child without them having to apply for one - they’ll usually get the number shortly before they turn 16 years old
If you choose not to get Child Benefit payments, you should still make a claim to get the other advantages.
I've seen that as my wife is registered as our disabled son's carer she automatically gets NI credits which is handy. I guess once he is 16 (in 7 years) I can just pay in every year the amount for a further year's NI until her retirement age which is still 26 years away (even if for 10 of those years we will likely be retired overseas in Thailand). Looks like she has been registered as his carer automatically for the last 3 years so by doing this she would get 29 years NI credit for her pension