I have two styles, each declared in its separate 3rd party control that don\'t play well together and I\'m not even sure why that is - and ultimately - how to make them work
You have to be more specific since both the rules are applied to your td. You can do it like this:
td
.myrow>td { background-color: #88f; } .myrow>td.ui-state-error { background-color: #f00; }
Here is the Updated Fiddle