Follow, I think you will be OK with a bit more time, some patience and a few minor tweaks. First, 20 psi is MUCH too high for your weight, IMO. That is a big reason why it bounces so much. The tires are a big part of the suspension on these bikes, and too much air will have the results you experienced. Retmotor mentioned 12/10 psi, and with your light weight I think that is about right. Particularly if you are riding at trail-riding speeds.
First, what kind of bikes and riders are you intending to keep up with? This is critical. Looking at your second picture, I assume that it is one of the easier sections. A bunch of guys on enduro or motocross bikes would often go through something like that at 30-45mph or more. A T-Dub would be uncomfortable at much beyond 20-30, and even then you'd need to dodge the bigger rocks. Pick the easiest line by going from side to side.(you probably know this)
Second, by "biker mogels" I assume that you mean "whoops" (whoop-de-doos) which is the biker term.8=) Moguls or whoops, on skiis or a bike, staying upright on them at speed is an advanced technique. The fast guys on the enduro bikes can skim over just the top of the whoops without dropping down into the lower parts between them. That takes speed, technique, and a much more expensive and better suspension than the T-Dub possesses. On a T-Dub I just drop my speed and ride up and down over them. Sometimes you can avoid doing that by just riding a bit to one side or another where the trail is more level.
IF YOU INTEND TO RIDE AT SPEED OVER WHOOPS, YOU DO INDEED HAVE THE WRONG BIKE. A word of caution. People can get badly hurt riding whoops, even with the right bike.
I'll wait for your answers before saying anything more.
First, what kind of bikes and riders are you intending to keep up with? This is critical. Looking at your second picture, I assume that it is one of the easier sections. A bunch of guys on enduro or motocross bikes would often go through something like that at 30-45mph or more. A T-Dub would be uncomfortable at much beyond 20-30, and even then you'd need to dodge the bigger rocks. Pick the easiest line by going from side to side.(you probably know this)
Second, by "biker mogels" I assume that you mean "whoops" (whoop-de-doos) which is the biker term.8=) Moguls or whoops, on skiis or a bike, staying upright on them at speed is an advanced technique. The fast guys on the enduro bikes can skim over just the top of the whoops without dropping down into the lower parts between them. That takes speed, technique, and a much more expensive and better suspension than the T-Dub possesses. On a T-Dub I just drop my speed and ride up and down over them. Sometimes you can avoid doing that by just riding a bit to one side or another where the trail is more level.
IF YOU INTEND TO RIDE AT SPEED OVER WHOOPS, YOU DO INDEED HAVE THE WRONG BIKE. A word of caution. People can get badly hurt riding whoops, even with the right bike.
I'll wait for your answers before saying anything more.