Elana it is perfectly possible to have a horse going forwards into a steady contact and still post to the trot. It is also perfectly possible to drive a horse forwards with your seat whilst rising to the trot. Infact If you can't keep your hands steady and give a contact whilst posting then you realy do need lessons.
Infact at this stage I would reccomend AGAINST sitting the trot as the horse is unlikely to have the back muscles to support a sitting trot, let alone a sitting trot in an outline. There is a reason that you are allowed to rise to the trot untill elementary level in dressage (I believe that equates to 2nd level in the US)
My youngster certainly won't be having me sitting his trot untill I have a correct and forwards outline built up and he already has a good topline and muscles and has been in disgustingly good health all his life. This mare has not been so fortunate in the past and is still recovering from that.