More common expression for "move your bowels"

Move your bowels may be too polite and sounds strained, and merely saying shit sounds offensive. What do native English speakers say then when you need to move your bowels, especially when a parent asks his toddlers whether they need to shit?

I'll assume you're talking about usage in mixed company where good manners are required. North Americans seem to use 'go to the bathroom' to cover a wide range of excretory and ablutionary functions, regardless of whether an actual bathroom is within walking distance. Brits might use the similar 'go to the lavatory' or 'go to the loo'. We Australians will typically say 'go to the toilet' or 'use the toilet' - 'toilet' being a word considered almost taboo in certain other English-speaking cultures - although 'bathroom' is creeping into common usage.

If you're talking specifically about bowel movements as opposed to urination, I wouldn't think there is a need to specify one or the other in polite circles. If with close friends or family, you might say something like 'do a poo' or 'take a crap'. There would be a thousand synonyms for 'having a shit' I'm sure.

In AmE, 'Poop' is the current terminology. That is, in a squeaky voice:

I have to poop

is what the kids say these days. Adults usually don't tend to feel like sharing the particular mode of ...export. They might euphemize even further and just say 'I have to go' or 'I really have to go'.

"Number one" for urinate and "number two" for defecate was the terminology I remember from childhood (but is also not childish and not taboo (that is, not like 'shit', it is very plain sounding))