Significance of Variables in Spatial Model

#1
I've encountered a (to me) seemingly strange phenomenon in my regression results and would like to just ask generally if this is actually a surprising/concerning result or if it's actually reasonable.

I am running a spatial lag and spatial durbin models (using the exact same dependent variable and explanatory variables for both). One of my explanatory variables is simply the number of doctors (per observation unit, which in this case is hospitals) and it is constructed by summing two variables which are the number of "Beleg" doctors (to my knowledge there isn't a great direct translation) and the number of non-"beleg" doctors.

I ran the lag and Durbin model using the total # of doctors as the explanatory variable first it was not significant (p value > 0.05 in lag and >.1 in Durbin).

I then ran both models again, but with the # of doctors separated into its components instead, so # of beleg and non-beleg doctors were used as explanatory variables. In both models both # of beleg and non-beleg doctors were highly significant (p-values < 0.01 in all cases).

In my mind this seems like it shouldn't be the case, but I'm not experienced enough to really be certain, so I was hoping someone could briefly comment whether or not this result is reasonable. If you are feeling generous an explanation of why it's reasonable or what I should check for if it isn't would also be appreciated. Thank you!