I use lard all the time and love how much time it gives me to play. I think you may be soaping too cool. 35 C is about 95 F correct? You may be getting a false trace because the lard is starting to re-solidify - so even though it looks like trace, it's really not. You may want to try going to about 105-110. When stick blending, just blend until emulsified and then try hand stirring. You could also try more water. Are you gelling the soap? Lard can have a fairly hot gel and that could be why it's separating. You could try not gelling to see if it does the same thing.
Goo luck! I hope you can figure out what's happening because lard makes a wonderful soap!