My only advice is to work on being strong in your own axis: focus on having a strong connection with the floor, keep your knees and ankles slightly soft, take care over your foot placement, keep your core muscles strong and lead from your centre. Shortening your steps slightly can help, so you are never operating at the limit of your balance when you commence the lead for a movement. (As an aside, a number of dancers that I respect greatly extol the virtues of Tai Chi as a method of developing strength of axis. Sadly, at the moment I don't have the time to try it myself.)
Sometimes, just sometimes, I feel as if my axis is so strong that nothing my partner, or anyone else, could do would threaten it. It's a wonderful feeling but only lasts for a few moments at a time - hopefully, as I dance and practice, it will become the norm. For the time being, when I'm dancing with someone "wobbly" I will focus on being strong in my axis and it seems to help a lot