If easy access to MRT is a priority, why not try Raffles the Plaza/Swissotel the Stamford, the Marriott or the InterContinental ,all of which are linked to MRT stations.
Since the OP is not comfortable taking a taxi with children, is it any safer boarding a SBS bus
Also bear in mind that thunderstorms are not infrequent in Singapore, and walking under the rain (or intense heat) from Orchard MRT to the Regent (with kids in tow) isnt exactly fun.
And as I have mentioned above, the Regent has not been a top property in town for a long, long time ...