My friend teaches English in Vietnam. One of the workbooks has a sentence to correct:
I will work very hardly, that will please my father, and I hope I will soon promoted.
She corrected it as:
I will work very hard, which will please my father, and I hope I will soon get promoted.
However, one of her students doesn’t believe that the switch from “that” to “which” is necessary. It seems to me that using “which” prevents a comma splice, but I’m not exactly sure why.
IANA grammatarian, but I think that the clause “that will please my father” is an independent clause, while the clause “which will please my father” is a subordinate clause. Indepentant clauses need to be joined with a conjunction, be split off as a seperate sentence or joined with a semi-colon. Subordinate clauses take the place of a part of speech in a sentence so they don’t make any sense as a seperate thought. I can’t work out what part of speech the “which” clause is, so I’m going with the old english class standby and saying that it’s an adverb clause modifying the whole predicate.
I’ll be that the reason that the student is confused is that the word “that” is often used to begin subordinate clauses, as in the sentence “The dog that stole my hat ran off to the north.” In this case, however, the clause “that will please my father” is a complete though on its own, and so it’s an independent clause.
sigh
I’ll bet
If the relative clause defines its subject, “that” should be used; if it merely describes its subject, use “which”. Fowler on the issue.
In the question, the relative clause (“which will please my father”) only describes the hard work, so “which” rather than “that” is correct. We could have “The hard work that I will do (as opposed to the work that anyone else does) will please my father.” to illustrate a sentence in which “that” would be correct.
However, we can still use “that” in the question, if we treat it as a pronoun and have two sentences rather than one. Another possible correction would be:
I will work very hard. That will please my father, and I hope I will soon be promoted.
We could put a semicolon rather than a period - “… hard; that will please…”, but a comma isn’t adequate to seperate these particular sentences.
Whether “I hope I shall soon be promoted” is a further necessary correction is perhaps too advanced an issue. 
Yup.
“I will work very hard and father-pleasingly”.
A good point about the original question. Why is the adverb “hard” and not “hardly”? Because English is Like That, and it’s the sort of thing that just has to be learnt rather than deduced logically.