How do I buy xbox live for a family member on my Microsoft Account

I can understand your frustration with that. This is what I found on the Points issues,

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How do I purchase Microsoft Points?

Microsoft Points are the currency of the Xbox LIVE Marketplace. Only the primary Family Pack member can purchase points, making it easier for a parent to manage his or her family’s entertainment budget.

Primary member: This is the Xbox LIVE account that you used to sign up for the Gold Family Pack membership. This account can purchase and give Microsoft Points to other family members (secondary accounts). How do I share points with family members (secondary
accounts)?

Secondary members: Secondary family members cannot use credit or debit cards to purchase Microsoft Points. Instead, secondary account members can redeem a Microsoft Points card (available at retail locations), or the primary member can give points to
secondary members.

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It would seem to me, it's more a security thing, I hope this helps you.

You can transfer Microsoft points when in a Family Membership IceStorm from the 'parent' account to one of the child accounts in amounts of 400 I believe.

Instructions on how to do so can be found here Xbox Family Pack | Xbox LIVE Membership | Gold Family Pack - Xbox.com.

How do I share points with family members (secondary accounts)?

The primary member on the Gold Family Pack membership can give Microsoft Points to other family members (secondary members), so that they can make purchases on Xbox LIVE.

Give points to family members

1. 1. On your console, sign in to Xbox LIVE using the Family Pack primary account (the account used to sign up for the Family Pack membership).
      
   2. Go to My Xbox and select Family Centre.
      
      
      

1. Select the member that you want to give points to.
2. Select Grant Allowance.
3. Follow the on-screen instructions to give Microsoft Points to the secondary member. Points that you give to a secondary member cannot be reversed later.
   

Note If you don’t have enough points in your account, you’ll be prompted to add more points before giving points to the secondary member.

Hi Carla! Here's a link that will allow you to purchase a xbox live gold members threw microsoft.

https://www.microsoft.com/en-us/p/xbox-live-gold/cfq7ttc0k5dj?activetab=pivot:gamesanddealstab

What do you mean when you mention 'buy xbox live' refers to xbox live gold?

You can by a 12 month live gold membership on the Microsoft store web site. Here is a link to the GB store:

https://www.microsoft.com/en-gb/store/p/xbox-live-gold/cfq7ttc0k5dj

There is an option to by as a gift:





Or... you should be able to by a membership card from your local store with a code you can redeem.