What test should I use?

I´m analyzing the following case: I have a continuous response variable, that allows positive, negative and null values; and factor's as explanatory ones. I thought of running a GLMM, as I have dependent data (one subject was measured more than once), but:

1. My response variable is more likely to have positive and zero values than negative ones, so I can´t assume the residuals would be normally distributed 2. I can´t use zero-inflated models as my response variable is not countable, but continuous 3. I can´t use a gamma-distribution as my variable allows negative values

What should I do? Also: I´m using R to run my tests, so any hints on how to perform your suggestions in that environment would be very appreciated! THANKS!