DT2 was horribly constipated last year - we tried disimpaction with movicol and it didn't work - she was taking 12 sachets a day by the end and pooing out water, but it hadn't touched the disimpaction at the top of the gut. (Btw she was 10, so far more able to understand that she had to drink this liquid, even though it doesn't taste that nice - we dilute it in blackcurrant squash.)
She ended up being admitted to hospital, and had something called Kleen Prep administed through a nasal gastric tube, as well as something called Picolax. She had to take 2 litres of the Kleen Prep over 24 hours. It's generally given to adults when they need a complete clear out ahead of something like a colonoscopy. Adults would have to drink it, but we knew there was no way she'd be able to drink that much, hence the NG tube. The worst bit was the tube being put in, but after that it was pretty painless. We were in a side room with a bathroom shared with only one other patient, which was absolutely necessary, as she was on the loo a lot!! We were in for 3 days and it really helped to clear the blockage. She's still on movicol - two sachets a day - but she doesn't seem to have any lasting constipation issues.
If you take your DD to A&E, I would ask for this procedure to be done - tell them that Movicol simply hasn't worked, and as she's so little, she simply can't drink all that she needs to in order for it to have any effect at all. I'm sure the dosage would be lower for her, but it would definitely be worth a try. (Btw, we're in North London and are under the care of a specialist paediatric gastroenterologist, whose details I can pass on if you'd like me to.)