It definitely sounds like you need a different saddle! The one you're riding is pretty narrow, and typically if someone's putting her weight on her genitalia rather than on her sit bones, it's because her saddle's too narrow.

Here's what I did: I sat on a piece of paper on my Pilates mat to make a butt print. (Sit on a low step-stool, or on a hard chair with your feet on a stool, to approximate a riding position.) While the indentations were fresh, I circled them so I'd have a permanent record of where my sitbones are. Then you can take that print and lay it over any saddle and see whether it's wide enough to support you.

Then there's pear shaped vs. T-shaped saddles, and the shape of the cut-out to consider. Just like trying on clothes, there's no substitute for trying on saddles. Many LBS's and many saddle makers will let you return a saddle that doesn't work for you.

I have to say this: your coach may be very good at teaching you to get stronger and faster, but he obviously knows nothing about saddles if he thinks he can look at one and say "it's a good seat" and therefore it ought to work for you. If he hasn't measured your sitbones, the Q-angle of your femurs, and the dimensions of your soft tissues he has no idea what saddles might work for you and what ones wouldn't.