But again, Libertarian is an ideology.
Not exactly, it's a philosophy not an ideology since it's easily (and best IMHO) applicable beyond the boundaries of political theory; it is based on the foundational principles of non-aggression and property rights, one (can) live ones life at all levels based on it's teachings.
When you use the term "conservative movement" what do you mean? Because when I think of a movement, it makes me think of ideological movements. Social conservatism is an ideological movement. That's fine, I have no problem with social conservatives just like I have no problem with social libertarians or even social liberals...
IMHO The "conservative movement" as generally understood casts as fairly wide net since it encompasses the ideas of a number of prominent conservatives of the last half century or so from the classical liberal bent of Senator Goldwater to the Paleo-Conservatism of Buckley and Kirk to the Social Conservatism of Reagan (and to a lesser degree Bush the Younger). All these "flavors" have at least one thing in common; adherence to principle over expediency, of course they also share a lot of commonality with respect to public policy and economic positions but the most critical thread that connects them are the principles which I pointed out earlier.
but our federal government is supposed to collectively represent us all, it shouldn't be guided by ideology. I'd rather have someone who isn't part of any movement and simply utilizes conservative philosophy and approaches to problem solving. I think Trump would be that kind of president.
What do you mean by "represent" ? IMHO Governments are not instituted to "represent" anything, they are instituted as a means for one group of people to band together in defense of their lives, liberty and property; going beyond those boundaries has historically led to oppression, disenfranchisement and ultimately dissolution. The intent of the founders was to create a Federal Republic with implicitly limited powers pursuant to those ends because they looked through the lens of history and attempted to learn from the mistakes of the past (see Roman Republic->Empire->Dissolution).
I agree with you though , it shouldn't be guided by ideology, it should be guided by both the letter of the law (in our case the U.S. Constitution) and the principles upon which the Republic was founded (specifically popular sovereignty and the primacy of individual liberty). The problem with Trump isn't his lack of ideology, it's his lack of any coherent set of principles coupled with his disregard for the rule of law; in this regard he's just like every other egomaniac populist demagogue in history and thus his future actions are completely unpredictable (since he has no boundaries).