How easy it is to get a US Visit Visa for an Indian (muslim) family based in Dubai?

We are a small family of three (DH, I and a toddler) and would like to visit my sister and her family in the US. We have previously been to a couple of places in Europe, Thailand and Mauritius, but this is our first visit to the US. I was denied a visit visa when I was single and living in India at the time. they said I did not show enough documentation to ensure i would leave. Fair enough.
Now we are based in Dubai and would like to know what are our chances. Oh, we are also muslim. We are a moderate family, I dont cover myself, we dont look overly Muslim but we are practising Muslims but look like regular people and dress in regular everyday attire. We are both college grads and speak very good, unaccented English.
We love to travel, have every intention to return to our fabulous life and career in Dubai and would just like to know how hard it would be this time around. What can we submit to make our case stronger? Any documents or papers that would help our case?
We were also denied a visit visa to paris in the week of Sept 11 before our daughter was born, it was a bit saddening because we wanted to visit the city of love, mean no harm to anyone and dont want to run away or end up on another country's charity so cant understand on what basis these countries make such decisions. Any inputs would greatly help! thanks in advance.

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