Question: I have been told that you always use 'beaucoup de':

I understand the below should use 'de'

J'ai mangé beaucoup de sandwichs
(I ate lots of sandwiches)

However, I was told even when you are saying 'lots of **the** sandwiches', you still use 'de', which I am not satisfied with:

J'ai mangé beaucoup **des** sandwichs que ma mère a preparé
(I ate lots of **the** sandwiches that my mum made)

Should 'de' be used in the above or can you use 'des' in a case when you are referring to specific things?

Answer: 
There are two aspects in your question:

1. the quantification over sandwich
2. the quantification over time

> 
> « J'ai mangé beaucoup de sandwichs que ma mère a préparés. »   
> 
>  => “I ate lots of sandwiches made by my mum.”
> 
> 
> 

This says nothing about sandwiches made by mum I did not eat and nothing either about how many times mum prepared sandwiches. I might have eaten lots of mum-made sandwiches over time.

> 
> « J'ai mangé beaucoup des sandwichs que ma mère a préparés »  
> 
>  => I ate a lot of the sandwiches my mum made.
> 
> 
> 

This says I did not eat all the sandwiches made by mum and also seems to imply that we are talking about one lot of sandwiches mum made that one time.

The first sentence is a sort of indefinite, the second is a sort of partitive.
When you are referring to specific things, you use definite articles. In the case of a plural, it is "*les*".

Now, "*beaucoup de les*" is unacceptable, since "*de les*" always contracts as "*des*".

In your example, the sandwiches are not generic; they are those your mother prepared, so a specific thing. Your example is perfectly fine!

Now, when speaking of generic things, this would be another business:

> 
> I ate lots of sandwiches.  
> 
> *J'ai mangé beaucoup de sandwiches.*
> 
> 
> 

It is however the same logic as in English. Your instinct seems better to me than what you were told. I cannot think of any counter example at the moment.