Am I being stupid (or Tyre fitting advice)

I'm fixing up an Islabike for my daughter, it came with 2 slightly knackered tyres so I'm replacing them. The wheels are 20", with the tyres on there 1.35x20's. Looking around I can't find much in that size so I'm going for some 1.75x20's instead. I've checked the metric size on the tyre (406) and the replacements (also 406) so I know that they should fit.
However, here comes the problem. The tyres appear to be too large for the wheel. I can roll them on by hand and when I pump up the tyre, one part always gets pushed off of the rim, like the tyre is too big for the wheel.
I'm used to 700c wheels/tyres where the biggest problem is getting the tyre onto the rim, pumping it up is the easy bit! So, am I doing something wrong or is the tyre the wrong size? If so, can anyone recommend a smaller 20" tyre?
However, here comes the problem. The tyres appear to be too large for the wheel. I can roll them on by hand and when I pump up the tyre, one part always gets pushed off of the rim, like the tyre is too big for the wheel.
I'm used to 700c wheels/tyres where the biggest problem is getting the tyre onto the rim, pumping it up is the easy bit! So, am I doing something wrong or is the tyre the wrong size? If so, can anyone recommend a smaller 20" tyre?
FCN3: Titanium Qoroz.
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schwalbe marathon plus at about £30 a pop are a very good tyre. Your issue is most 20" bikes have fatter tyres on them so they look like a cool mountain bike.
Isla bikes puts something sensible and effective on, but not as readily available .
Might be worth asking on the family and kids section what people use / where they buy them as there are a number of isla bike owners on there.
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