"My children can now swim."
Translation:I miei figli adesso possono nuotare.
i am guessing you are asking if these three can be correct:
Ora i miei figli possono nuotare.
I miei figli ora possono nuotare.
I miei figli possono nuotare adesso.
Just so everyone knows, there are to versions of 'can' in Italian: this one, possare, actually doesn't mean 'is able to' (as you might expect from the context) but instead means 'is allowed to'. Pretty misleading, and they should definitely accept both here.
I think you mean 'potere'. 'Possare' doesn't mean anything :-)
In this context, 'possono' means both to have the permission to and to be able to (just like in English).
I thought that with close relatives it was not necessary to use the definite article. Does this only apply to specific relatives such as brother or sister?