I asked the RCSLT about this last year and was told:
“SLTs who wish to commence practice outside of the UK via telehealth/telepractice would need to be complying with the guidelines set out by appropriate regulatory body of the country in which they would be providing therapy prior to providing any services (including those delivered via telehealth).
With regards to insurance to do this, the cover you receive through your RCSLT membership does cover this under the ‘incidental work abroad’ clause excluding USA and Canada. However, incidental work is defined as a short period of no more than 12 months, so you would need to be aware of this and plan for onward referral etc if treatment would exceed this.”
So it sounds like you just need to check Italy’s SLT guidelines. The 12 month rule sounds like you would be fine to continue with the family for a while, especially if they are looking to move on to an in person therapist.