In my experience with dealing with multicollinearity, often removing one collinear variable from the model results in the other collinear variable(s) becoming significant (assuming that all the collinear variables are significantly correlated with the dependent variable bivariately.
However, I've recently encountered a situation where I have a model shown below in which $X_2$ and $X_3$ are highly correlated ($r > 0.95$) and the tolerance scores for the two variables are below $0.1$
$$ Y = \beta_0\ + \beta_1X_1\ + \beta_2X_2\ + \beta_3X_3\ +\beta_4X_1X_2\ +\beta_5X_1X_3\ $$
*all variables are continuous.
The results of the regression model show that all 5 slopes are significant (3 slopes for the main effects and 2 slopes for the interactions). One of the possible solutions is to remove one of the highly collinear predictors. If I remove one of them - say $X_2$, I get a new model as shown below.
$$ Y = \beta_0^\prime + \beta_1^\prime X_1\ + \beta_3^\prime X_3\ +\beta_5^\prime X_1X_3\ $$
After $X_2$ is removed, while $\beta_0^\prime$, $\beta_1^\prime$, and $\beta_3^\prime$ are significant, crucially, $\beta_5^\prime$, the slope for the interaction term, is no longer significant. The same thing happens if I try to remove $X_3$. So I wonder what may be the reason that causes this pattern to arise and how it can be potentially dealt with. Thank you in advance!