I believe the *2 in your p-value calculation is erroneous.
Also, your parentheses are improperly nested. You are getting the normal probability for estimate/se_hat - pnorm(-estimate/se_hat)*2
The correct form should be 1 - (pnorm(estimate/se_hat) - pnorm(-estimate/se_hat)). Note, however, that this requires that estimate/se_hat be a positive value.
This is why I recommended earlier using a different approach. My suggestion is agnostic to the sign of the test statistic.