Ok, it's the rims, not the tyres. A set of steel beaded Stelvios were just as tight, needing the VAR lever again. Looks as if the 16" Sun CR18 causes problems for a lot of people. It's the shape of the rim channel that's the problem.
I am just having problems with a Sun CR18 rim in 559 size. I've already knackered one tube (humour not helped by a: the rim needing a Presta valve and all the spare tubes are Schraeders, b: the garage being very cold, c: I'm 900kms from home so don't have access to my usual fettling kit, of which there is lots).
The tyre is a B Twin 26"x1.75 which is not new and has never posed a problem in the past - they are on most of the girls' bikes. It has just come off a generic mtb rim (I will check the type shortly). Fitting to ZAC 19 and ZAC 2000 rims, among others, is a hands only job although levers are necessary to get them off. The Sun rim requires a lever to fit both beads!
My preferred tyre levers would be some light motorbike ones. They are back in Limoges. The job needs to be done by tomorrow, going home on saturday. The new wheel is a 48 spoke job from SJS, bought to resist 18kgs of toddler bouncing in a child seat over Kidlington roads. Might seem like a bit of overkill but the old wheel (32 spoke) suffered a serious spoke breakdown and so sledgehammers cracking nuts seemed a safer way to go. I am thinking of opening out the valve hole but with 48 spoke holes the rim probably needs to keep all its remaining metal so best avoided. In my absence a shop will have the puncture fixing job, daughter has more worthwhile uses of time than wrestling with this beast, even if she is well capable of handling most, if not all, conventional bike work.