How to wire new pendant lights to an existing ceiling light that has two different switches and have them work independently?
I think by reading your question that you have one light fixture controlled from two locations with 3-way switches. If that is true then you should have enough conductors between the devices and fixture to do what you want if can you tap your new pendant fixture off of your existing lighting fixture.

You can replace the 3-way switches with standard switches and arrange the wiring to switch the existing fixture with one switch and the new with the other switch. It would be a matter of tracing, sorting and marking the wires correctly to achieve this task. 

Of course I can't tell you exactly how to do it since your question doesn't provide enough information. That would require much more information and perhaps some pictures. 

FYI - A "pro" as you say could probably trace, sort and mark the wires in less than an hour if knows what he is doing and was on site. Of course installing fixtures in an existing ceiling would take some time and depend on existing circumstances. So call a pro or try to sort your way through it? The answer would be based on your experience and ability as an electrician, and your willingness to take the time to do the research and post it on this type of site.

Hope this helps.