Satterthwaite degrees of freedom in nlme multilinear model in R

Question

I'm working on a data with milk composition analysis and I want to analyze relation between them. I have 270 observations and a categorical variable "Primimulti" with 2 factors. I created a regression model with nlme which allow me to add random effect and correlation structure. As you can see below, I also ad a polynomial to the temporal variable.

lm_corCAR1<-lme(lactom ~ 1 + K + Na + Cl + LgSCC + Primimulti * poly(Jplus,degree=5),
                random = ~ 1 |  vache,
                corr = corCAR1(form= ~ Jplus | vache), 
                method="REML",
                na.action=na.omit,
                data=data_lait)

I obtained these results:

summary(lm_corCAR1)
Linear mixed-effects model fit by REML
  Data: data_lait 
        AIC       BIC   logLik
  -362.6679 -327.0227 191.3339

Random effects:
 Formula: ~1 | vache
        (Intercept)   Residual
StdDev:  0.08239433 0.09041495

Correlation Structure: Continuous AR(1)
 Formula: ~Jplus | vache 
 Parameter estimate(s):
Phi 
0.2 
Fixed effects:  lactom ~ 1 + K + Na + Cl + LgSCC + Primimulti + Jplus 
                    Value  Std.Error  DF  t-value p-value
(Intercept)      6.042503 0.18637710 233 32.42084  0.0000
K               -0.000381 0.00009654 233 -3.94676  0.0001
Na              -0.000444 0.00014290 233 -3.10745  0.0021
Cl              -0.000233 0.00005300 233 -4.40261  0.0000
LgSCC           -0.025792 0.00481912 233 -5.35193  0.0000
Primimultiprimi  0.008316 0.03783433  28  0.21980  0.8276
Jplus            0.000341 0.00009325 233  3.65468  0.0003
 Correlation: 
                (Intr) K      Na     Cl     LgSCC  Prmmlt
K               -0.928                                   
Na              -0.274  0.033                            
Cl               0.040 -0.179 -0.376                     
LgSCC           -0.073  0.127 -0.256 -0.053              
Primimultiprimi -0.368  0.184  0.485 -0.240 -0.035       
Jplus           -0.520  0.555 -0.104 -0.082  0.116  0.044

Standardized Within-Group Residuals:
         Min           Q1          Med           Q3          Max 
-3.601914552 -0.588982667 -0.001149027  0.652410609  3.296120444 

Number of Observations: 268
Number of Groups: 30 

But the DF are very high unless for Primimulti variable.

I tried to use satterthwaite to corrige the method of calculation for ddl but it doesn't change anything to the df:

model_parameters(lm_corCAR1, df_method = "satterthwaite")
# Fixed Effects 

Parameter          | Coefficient |       SE |         95% CI |     t |  df |      p
-----------------------------------------------------------------------------------
(Intercept)        |        6.04 |     0.19 | [ 5.68,  6.41] | 32.42 | 233 | < .001
K                  |   -3.81e-04 | 9.65e-05 | [ 0.00,  0.00] | -3.95 | 233 | < .001
Na                 |   -4.44e-04 | 1.43e-04 | [ 0.00,  0.00] | -3.11 | 233 | 0.002 
Cl                 |   -2.33e-04 | 5.30e-05 | [ 0.00,  0.00] | -4.40 | 233 | < .001
LgSCC              |       -0.03 | 4.82e-03 | [-0.04, -0.02] | -5.35 | 233 | < .001
Primimulti [primi] |    8.32e-03 |     0.04 | [-0.07,  0.09] |  0.22 |  28 | 0.828 
Jplus              |    3.41e-04 | 9.32e-05 | [ 0.00,  0.00] |  3.65 | 233 | < .001

# Random Effects 

Parameter             | Coefficient
-----------------------------------
SD (Intercept: vache) |        0.08
SD (Residual)         |        0.09

Uncertainty intervals (equal-tailed) and p-values (two-tailed) computed using a Wald t-distribution
  approximation.

I don't know what to do. Can you help me?

Thank you!