LMM model with nested design and random slopes (nlme package) cannot run with autocorrelation term

Despite many efforts, I cannot run a linear mixed model because of the autocorrelation term. In fact, I can't manage to code for both a nested design and random slopes within it.

For example, let's imagine some monthly captures of wild rabbits in kilograms in 5 sites during 21 years:

site<- rep(rep(c("Golden Cave","Ringo's place","Damned Dam","Knockampton","Easy Fuzzy"),each=12),21) 
year <- rep(2000:2020, each=12*5)
month <- rep(seq(1,12),21*5)
rabbit_captures <- rnorm(12*21*5, 50, 10)
dataset <- as.data.frame(cbind(site,year,month,rabbit_captures))
dataset$rabbit_captures <- as.numeric(dataset$rabbit_captures)

Then is the modeling part that I can't succeed:

library(nlme)
library(MASS)

model_lme <- lme(fixed = log(rabbit_captures) ~ site,  
                 random = ~ site|year/month, 
                 correlation = corAR1(value = 0.9, form = ~ site|year/month), 
                 data = dataset, method = "ML",  
                 control = lmeControl(opt = 'optim'))

I desperately get an error that I suppose is for the "site" variable within the autocorrelation structure term:

Error in as.character.factor(X, ...) : malformed factor

I can run the model without autocorrelation:

model_lme_wo_autocorrelation <- lme(fixed = log(rabbit_captures) ~ site,  
                                    random = ~ site|year/month, 
                                    data = dataset, method = "ML", 
                                    control = lmeControl(opt = 'optim'))

And I am really interested in including autocorrelation to compare both models.