I see it, and it sucks. But his administration gets certain things done and keeps certain other things from being done, and we only have him and the liberals to choose from right now. Unfortunately if you want certain conservative policies to continue being implemented, then you only have one choice.
How does it work in the UK? If you don't like any of the voting choices near the election time, can you successfully write in someone new and they get elected? That's awesome! But we don't have that here.
Although the UK and US are two of the longest established democracies in the world there are stark differences and it’s quite difficult to answer your question without a long explanation however I will try and give you a short answer.
Our Prime Minister (PM) is not like your President insofar as the PM is just the leader of their party and it's the party that has the power not the PM, and yes, the PM can be changed even during the elected term of the government. The power of the party is also dictated by the size of the majority they have in parliament i.e. the number of constituencies they gained in the general election and therefore the number of MPs (Members of Parliament) they have.
Each or our political parties has a leader, elected by the party membership. The leader of the party in power (currently the Conservatives) is called the Prime Minister and the leader of the largest losing party is called the leader of the opposition. The leaders of the smaller parties are simply called the leader of the ‘name of their party’ i.e. leader of the Liberal Democrats.
Each party will try to field a leader who they believe has the best chance of winning a general election and get their party voted into power. The leader of a party only holds that position for as long as their party has confidence in them and that includes the elected leader (the Prime Minister).
The party leaders who lose in a general election will often resign from their post because it’s clear they didn’t have the confidence of the electorate or otherwise their party would have been elected into power (or at least done well in the election). A sitting leader (PM) will invariably also resign if they lose the support of their own party because they are politically ineffectual or because of some embarrassing revelation in their private or public life, and/or if they lose a parliamentary vote of no confidence in the government. A motion of no confidence in the currently elected government can be made by any Member of Parliament (MP), irrespective of whether they are a member of the elected government or not. If such a motion is agreed to all MPs vote on whether they have confidence in the government and if the government lose that vote (on a simple majority basis) then it is normal for the PM to resign and will most often result in the current government being dissolved and trigger a fresh election.
I hope this sort of clarifies things.