You've got the good cable, and proper tools. Even good cable, improperly terminated won't yield a satisfactory signal. One splitter is better than many, because you have less connections, however you can't go indefinitely without a distribution amplifier.
Not knowing the construction of your home, all I can say is be careful when you start drilling through structural members or penetrating drywall between the garage and the house.
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There ain't nothin' more powerful than the odor of mendacity -Big Daddy
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