That doesn't sound right at all.
Have you tried treating the hypo with anything else instead of glucotabs? They aren't actually the easiest thing to chew, and especially when you are hypo. When I'm properly hypo, I have severe difficulty chewing. However - chewing is good, because the glucose starts to be absorbed through the inside of the cheeks direct into the bloodstream.
Does she like orangey drinks? cos my hypo treatment - and it works! - is Orange flavour Lucozade - it doesn't have the 'slightly strange' or rather 'unique' flavour of Original at all - it's just mega- orangey - and orange pop has always been my favourite since I was your daughter's age. 100ml of it is 15g carb. 100ml is a good drink and it's best if she isn't too hypo, if she swills it round a bit before swallowing. Failing that there are some good fruity flavoured glucose gels about these days - can't give you names but people like the Tour de France cyclists use them for energy whilst on the road, some have screw caps. Diabetics running marathons and that sort of sport, use them along the way - prevents them going hypo for starters and also provides extra glucose when their BG is OK.
So OK maybe the constipation isn't anything to do with the diabetes - it's not a usual scenario - but it's certainly caused by something - or lack of something, eg does she eat plenty of fruit and veg, and is she active, getting plenty of exercise, does she drink enough water and all the usual suspects? And what does your GP suggest?
The only other thing I can possibly think of which is D related is gastroparesis, which could account for hypos and constipation at different times - but as it's autonomic neuropathy that causes it for us (though non-D's cab get it too) it would be most unusual I think in a child of her age with D of only 4 years duration - and I wouldn't get jumping to any conclusions.
Finally you may have observed, we don't actually specialise in kiddies and there may well be something else a child might get, that I wouldn't know about. as I never had D as a child, have never personally known a diabetic child and I'm relatively ancient. There is however a UK mailing list of Childrenwithdiabetes, and you might perhaps have more success having a trawl round that or asking your question there?
I hope you find your answers.