The goal of partnership dancing is to be "one" (a single entity) on the dance floor. I always say, "Become a four-legged animal". Partnership dancing is NOT two jazz dancers that just happen to be touching each other and it is NOT two people dancing patterns in front of each other. To become a single entity you must be physically and mentally "one".
Sometimes it is necessary to switch between partnership and solo dancing. When dancing American Smooth, for example, you can go from partnership to solo and back to partnership, etc. There are three centers of gravity. You have a center of gravity, your partner has a center of gravity and the partnership has a center of gravity. When you partnership dance you should feel the partnership move, not just feel yourself or just your partner. All partnership movement should be referenced to the partnership's center of gravity and solo movement referenced to your personal center of gravity.
Most dancers have a hard time changing from solo movement to partnership movement. It is important to realize that what you feel when practicing by yourself and what you should feel when dancing in partnership is very different. Dancing takes a lot of practice to get the movements into muscle memory, but you want to get the feeling of the partnership into muscle memory not just the feeling of your half of the movement. Do not try to make your partnership movements feel like your individual practice movements.
You must remember that you now have four legs and the body above two of the legs is always counter balancing the body above the other two legs. So theoretically if you stand in dance position and simply release the frame each two-legged animal would fall slightly away from each other because they were counter balancing each other through the partnership center of gravity.
You don't think of leading your partner or following your partner, you should think of being part of the movement of the partnership. This means counter balancing your other half, supplying power to the partnership, leveraging off each other, using all four legs, etc.
You must change your thinking from being a "two-legged animal" to becoming a "four-legged animal". You don't dance yourself. You don't dance your partner. You dance the partnership as a whole.