These sentences are grammatical:
I used to have finished my work by the time she came home.
I used to be reading a newspaper by the time she came home.
Your alternant, however, is not grammatical:
I used to be reading a newspaper when she come home UNGRAMMATICAL
You cannot use "when she come home" to mean "when she used to come home". That's because "when" is not a conjunction.
Now compare that to this sentence:
She used to come home and wash her clothes.
This is grammatical. It is similar to "She used to come home and she used to wash her clothes".