Why can't I say "Ma copine et moi *nous* serons..." ?

​Actually, here the rule is the same as in English:
​though in spoken French, a lot of people would "double" the compound subject by adding its equivalent subject pronoun (Marie et moi, nous.... / Ta mère et toi, vous... etc), this is a redundant and incorrect turn of phrase, and it is to be avoided in written form.