Is it true that if the woman's side breaks off the engagement, she must return double?

That is a custom of some Malay communities, not a binding ruling of the Shariah.
By custom, if the man's side breaks it off, his gifts are forfeited; if the woman's side breaks it off, she returns the gifts double. Islam respects ʿuruf (custom) that does not conflict with the Shariah, and this custom can take effect if both families did agree to it at the engagement. But it is not a religious obligation. Islamic family law in Malaysia only mentions the return of engagement gifts (or their value) and expenses incurred in good faith, by the party who breaks the engagement without a valid reason. If the two families disagree about the amount, take it to the Syariah Court or negotiate through sulh (mediation). Ideally, the agreement on this should be recorded at the engagement ceremony to avoid disputes.