When performing hip inward/outward rotations, pressure in the knees indicates that you are pushing further than your hip flexibility allows. This may cause knee problems, and does not increase hip flexibility - so my advice is to be very attentive to this.
Note that building flexibility is different from building strength - you do not progress more with stronger exertion, but on the good side, you can practice much more frequently because less restitution is needed. Try doing e.g. a static version of the swivel hips for a 30-60 seconds twice a day to both sides, but using no force to press the knees towards the floor. That should increase flexibility rapidly.
(PS I am a complete newbie at GST but a long-time yoga practicioner).