It is possible to book two different places at once, but you're not eligible for a refund if you cancel one of them. Also, Third Party bookings are technically against the rules - if you're staying with two separate hosts, it's better if your family member creates an account to make the booking separately.
Yes, @Tim66 , it is so much easier in the long run to get your other family member to set up an account in order to book the second place. You can certainly help with that if they are not computer savvy. There may even be a first-time user referral credit in it for you and them. Look into that before you start the process. Go to your profile photo and click "Invite Friends" in the dropdown there.