Transferring from Bank of China in Hong Kong to Bank of China in mainland China is quite smooth, with no handling fees and normal exchange rates. After the funds arrive, you can search for foreign exchange services in the app, and after exchanging it, you can use it for normal consumption. This is a cross-border transfer that arrives in one working day, so exchanging USD in the future isn't as risky as imagined.
Another method is for your family member to apply for a Chinese bank card in mainland China. You can then transfer to their card, which effectively gives you an additional $50,000 in exchange quota, making it sufficient for household expenses.