I'm sorry, my son is a bit lively. I hope he doesn't disturb you.
vi-VA-ce — stress on second syllable. dis-TUR-bi — stress on second syllable.
When sitting with children in a carriage with other passengers — a proactive, courteous gesture.
'Vivace' (lively) is a diplomatic word for an energetic child. 'Speriamo non disturbi' (I hope he doesn't disturb) uses 'sperare' (to hope) + subjunctive 'disturbi'. This pre-emptive apology is a sign of Italian social courtesy and usually generates goodwill from fellow passengers.
Se il bambino dà fastidio, me lo dica pure.
If the child bothers you, please tell me.
Showing willingness to manage the situation
Purtroppo è difficile viaggiare con bambini piccoli.
Unfortunately it's difficult to travel with small children.
Fellow parents will empathise
Mi scusi per il disturbo.
I'm sorry for the disturbance.
General apology after any disruptive episode
Italian culture is very child-friendly — bambini are celebrated rather than merely tolerated in public spaces. Fellow travellers are usually understanding of children's behaviour on trains. However, the quiet carriage (vagone silenzio) is strictly adult-oriented. Families with children are encouraged to use the family compartment or the bar carriage area.