So your goal is to say if two regresson coefficients are significantly different? If so: you have from both regression models the coefficient (beta) and the standard error of this coefficient (se). Assuming that the distribution of the betas is approximately normal (e.g., if both regression analyses rely on more than 30 samples) you can calculate it in R in the following way using a z-statistic:

SE <- sqrt(se1^2+se2^2) #that is the approximate standard error of the difference

z<-(beta1-beta2)/(SE) #that is the z-transformed difference

p <- 2*pnorm(-abs(z)) #that is the p-value