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I'm not sure but here is the best solution I can provide:

I feel sort of optimization should be used to solve this issue, or definitely better model (rather then linear OLS model) but nonlinear...

data$retA <- with(data, as.numeric(c(0,diff(A))/lag(A,1)))


diff_binAB <- with(data, unique(diff_AB))
mse <- numeric(length(diff_binAB))

for(i in 1:length(diff_binAB)){
    pwise <- with(data, lm(retA ~ diff_AB*(diff_AB < diff_binAB[i]) + diff_AB*(diff_AB >= diff_binAB[i])))
    mse[i] <- summary(pwise)[6]
   }

mse <- as.numeric(mse)
mse 

diff_binAB[which(mse==min(mse))]
# -0.07

diff_binAC <- with(data, unique(diff_AC))
mse1 <- numeric(length(diff_binAC))

for(i in 1:length(diff_binAC)){

    pwise <- with(data, lm(retA ~ diff_AC*(diff_AC < diff_binAC[i]) + diff_AC*(diff_AB >= diff_binAC[i])))
    mse1[i] <- summary(pwise)[6]
   }

mse1 <- as.numeric(mse1)
mse1 

diff_binAC[which(mse1==min(mse1))]
# 0.04 

Here the results would suggest that the return (rate of change) is explained if the difference between A and B is at -0.07 (negative difference) and 0.04 with possitive difference between A and C.