How can I use my iTunes money for my own purchases when i'm part of family sharing?

His card should not be added to your account for any reason, in Family Sharing, the card on his account is automatically used for payment for purchases by other users in the Family Group, there is no need to added it to each user's account. Seems like there's some mistake in how things are set up here.

But even if his card is added to your account, account balance is automatically charged first regardless.

Is his Apple ID signed in to Settings ➜ Apple ID ➜ Media & Purchases by any chance?

If not, its just verifying the organizers card, but should not actually charge it.

If you follow the steps in the support document linked below, what payment methods appear for you?

click here ➜ If you need to change or update your Apple ID payment method - Apple Support

It should list your balance first, and then any added payment methods to the logged in account.

Even if it asks you to verify his card when making a purchase, Account Balance is always charged first. So you should be able to verify it, and have the purchase charged to your balance and not his card.

This happens automatically, and there's nothing that needs to be done. Account balance is always charged first before any other payment methods are actually charged regardless of any verification needing to be made before the purchase completes.

You should be able to remove his card from your account and not affect his account in any way.

Your iTunes account balance will be automatically charged for your purchases as long as there is enough money for it.

Otherwise, it will charge as much as it can to it, and then charge the Organizer's payment method for the rest.

This however, has no bearing on whether or not the Organizer needs to approve the purchase if Ask to Buy is turned on, or if the Organizer's payment method needs to be verified for any reason.

If Ask To Buy is turned on, then the Organizer will need to approve the purchase, but once approved it will be charged to your account balance.

If the Organizer's card needs to be verified, then you will need to do so, but once verified, again, it will be charged to your account balance automatically.

Having to approve the purchase or verify the organizer's payment method does not mean it will charge that payment method.