There will be no problem at all.
Obviously, miles will be accrued only where the skywards account is matching the passenger name.
If you wish you can create other accounts for your husband and daughters and add their skywards account as well.
. The OP can earn miles for him/herself on her families tickets as well (20% actual miles) if they are registered as family members under OPs master account (but then her family earns no miles of their own, OP earns them all