I've got one fussy eater (DS1) and one coeliac (DH) so I'll do my best to collate my experiences of both!
Firstly, the fussiness might possibly be linked to the coeliac disease- if he's been made uncomfortable by certain foods it may have led to reluctance to eat. Lactose intolerance is common in undiagnosed coelicas so maybe when his insides have healed up he will be happier to drink milk. Of course, he may just be a typical fussy toddler!
Here are some ideas of gf foods that my fussy child would eat.
Pancakes made with doves farm flour- I sometimes make American style ones and sneak in grated apple or very well puréed sweetcorn. A good Sunday morning breakfast!
Fish or chicken goujons made by coating with gf flour, egg and crushed cornflakes or rice crispies (make sure these are gf, not all are).
Rice cakes are not very nutritious but can be covered with Philadelphia or peanut butter for a snack.
My fussy child likes banana milkshake with peanut butter. I also add malt extract for him but that's obviously not suitable, will try to think of an alternative. Might be a good way of getting milk in though.
I'm sure there's plenty more that I can't think of at present!
We've found that gf food has improved immensely even in the 5 years since DH was diagnosed. In particular Genius bread (although now supermarkets are making own brand breads that are also very good), doves farm flours and cereals, and Salute pasta. (DH also has his favourite biscuits and cakes but probably not a good idea for your toddler!)
It is incredibly daunting at first but you do get used to it. I find that at home I hardly think about DH being coeliac, just make 'normal' food and substitute where necessary. It is more tricky when out, you do have to be more prepared with snacks and gf sandwiches etc.
Hopefully some of this rambling will be helpful- if I think of more ideas I'll come back!