Inflating toddler tires I got my toddlers bike second hand &amp; it looked like tyres were a bit flat. We brought new tubes &amp; when I went to replace them I found that the current ones inflated.  It seems that I can pump &amp; pump &amp; still no more pressure is added past certain point. I.e., one can still depress a section of a tyre so the sides meet.  When daughter is on the bike it looks like there is no air. With a single finger &amp; minimal pressure I can flatten the tyre to the rim. 

Is this normal or what am I doing wrong?
Might be that both tubes have punctures, perhaps because they are old and have cracked. 

Might be you are not getting the pump on the valve properly. Most kids bikes use the wider Schaefer type bales, made sure you are using the correct pump head. 

You can try taking the bike to a local bike shop, the usually have a good floor pump with s pressure gauge for free use.