Try fixing the HTML errors on your web page. (There are not too many so it should not take long but the errors that currently exist may be causing problems.) Different browsers may be more tolerant towards errors than others.
This may or may not help but, even if it does not, once the errors are fixed, your web page should be rendered with greater predictability and consistency across different browsers and we can then eliminate HTML errors as being a possible cause of your problem.
You can check the code on your web page using the W3C Markup Validation Service and then fix the errors reported.
Also, rather than load your gallery into an iframe whose dimensions look to be set dynamically by JavaScript, you might like to try embedding your gallery directly into your web page by following the baseUrl embedding instructions here.
You could also check to see if your problem happens just in Mobile Safari or in Chrome, too.
Also ... when the galleries load on iPad, the first image doesn't load. Just a black screen.
This sounds like you may be viewing your gallery over a 3G/4G connection (rather than wi-fi). If this is the case, then please see this FAQ which has a solution: Why can't I view my gallery on a 3G mobile connection?