How to make a model applicable to Turing.jl?

No problems storing duals in either Dicts or DataFrames:

julia> using DataFrames, ForwardDiff

julia> DataFrame(x = [ForwardDiff.Dual(0, 1)], y = [Dict(1 => ForwardDiff.Dual(1, 2))])
1×2 DataFrame
 Row │ x                   y                                 
     │ Dual…               Dict…                             
─────┼───────────────────────────────────────────────────────
   1 │ Dual{Nothing}(0,1)  Dict{Int64, ForwardDiff.Dual{Not…

so you’ll have to give us an MWE to help.