The preposition that goes with "responsible," that connects it to its complement, is "for." "For" is followed by a noun, a noun phrase, or the gerund form of the verb.
"¢ You Are Responsible for Making
Sure Our Mail Gets to You. Posted Aug 26, 2004, 1:45 AM ET by Anne P. Mitchell, Esq. ...
If "responsible" is followed by "to," the "to" is a preposition, and its object refers to the person or persons owed the responsibility.
"¢ "When asked to define responsible government, most people intuitively think that it means that government is responsible to the people
it governs" www.mapleleafweb.com/features/democracy/responsible.htm
Or, the prepositional phrase with "to" (referring to the people) is then followed by one with "for," showing what the responsibility refers to:
"¢ Recruit Petty Officers are responsible to RDCs for the proper execution
of any orders they receive. ... The Recruit YN is responsible to RDCs for: ... www.nsgreatlakes.navy.mil/recruitjobs.html
You can see examples of "responsible for" in several references, including these:
"¢ the American Heritage Dictionary, in an example in the usage note: "I am responsible for the ship's safety"
"¢ the Collins COBUILD entry for "responsible": "If you are responsible for something.....,"
"¢ the BBI Dictionary listed under "responsible": "responsible for"
"¢ the Longman Essential Activator: "be responsible for something"
"¢ the Cambridge Grammar: "Adjective + 'for' : responsible....."
In spite of the fact that all references that we consulted show "responsible" as an adjective followed by the preposition "for" + a noun or a gerund, there are numerous examples on Google showing "responsible" + an infinitive, as in Version 1 of your example sentences:
"¢ After an engagement, who is responsible to make the first overture to the other family, the parents of the bride or the parents of the groom? http://www.faqs.org/qa/qa-9225.html
This sentence could also be constructed – better constructed, according to our references -- : After an engagement, who is responsible for making
the first overture....."
The American Heritage Dictionary of the English Language, Fourth Edition Houghton Mifflin Company. 2003
The Collins COBUILD English Dictionary. HarperCollins. 1995
The BBI Dictionary of English Word Combinations, by Benson, Benson and Ilson. John Benjamins. 1997
The Longman Essential Activator. Addison Wesley Longman Ltd. 1997
The Cambridge Grammar of the English Language, by Huddleston and Pullum. Cambridge University Press. 2002