A cash ISA would be owned by your daughter and the allowance is subject to her personal 'adult' ISA allowance and does not impact upon a JISA, which is managed by a person with parental responsibility until the child is 16.
JISA contributions can be made up until the child is 18, at which point it becomes theirs absolutely. It is therefore possible for your daughter to open a cash ISA while you make contributions to her JISA.
Under the tax rules that apply when income is received by a child on capital gifted to them by a parent, a child is deemed to be anyone who is under 18 and unmarried. You therefore need not worry that income generated from a gift to your 18-year-old son will incur income tax for you.
There could, however, be other implications such as inheritance tax, access and gifts with reservations rules to consider.