Multinomial Fixed effect regression

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I am new to R, I am trying to run a multinomial fixed effect regression. I am using the feglm function from'fixest' package. This is the model,

reg<-feglm(diar~c1+c2+rural+c1rural+c2rural+religion+wealthindex+extendedfamily+genderchild+agechild+birthorder+factor(ageofmotherFE)+factor(surveyyearFE)+factor(divisionFE),data=d7,family="binomial",cluster=c('rural'))


The dataset is the DHS questionnaire which is a repeated cross sectional. I am exploring the impact of mothers education on child health. 
Dependent variable: is categorical, did your child have diarrhea in the last 2 weeks?
Independent variables: c1= dummy variable, mother belonging to cohort 1
                       c2= dummy, mother belonging to cohort 2
                       rural= dummy, mother residing in urban or rural area
                       c1rural, c2rural= interactive term, dummy
                       genderchild, agechild, birthorder= numeric

Control variables: religion=dummy
                   wealth index= categorical
                   extended family= dummy
Fixed effects: age of mother, survey year and division(geographic)


My questions are: 
1) I know family will not be binomial but What will be the family for multinomial ? 
2) Is my model correct? I have looked into bife and clogit but they do not fit my requirements. Are there any other better options.
Thank you
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