I think you shouldnt think that the second is the MAIN verb. Main verb, i mean the real activity.
I go to home << activity is "to go"
I go to shopping << activity is "to go"
I want to go << activity is "to want"
You come to us << activity is "to come"
but if you say:
I go to the shop which is near to stadium << here activity is still "to go", as you see there is one more verb "is" (to be), but it is not the main verb. I mean not the activity of the main sentence.
I want to go swimming << activity is "to want". You may go or not, so go is not the main verb, or "swimming"
yüzmeye gitmek istiyorum
Lets look at this "SOV" stuff:
Subject + Object + Verb
Since we know that Subject in Turkish can be hidden, so we may not see it(it is possible that we cant find it in the sentence).
Now the most important part: Verb
Look at our previous example:
I want to go swimming
As i wrote before, here, the main verb is "to want": istemek
So now, you can think that the others are the verbs of other sentences(clauses) which are to complete the full meaning.
We will put this verb "istemek" at the end with the true suffixes.
Now we have to know the Subject in order to put true suffixes. It is here: "I", so it would be:
istiyorum.
Now we can go on with the rest: Object
It is: to go swimming
Pay attention: here is another two activities now: "to go" and "to swim".
We are talking about swimming but the first idea is "to go": gitmek
We use "istiyorum" with verbs directly:
gitmek istiyorum
and the last part: swimming. this is the part of the activty "to go", it must be like the other "to go" examples:
i go to the cinema:
sinemaya giderim
It goes with the suffix: "-(y)a", so "swimming": yüzme
it must be: yüzmeye
Let's complete it:
(Ben) yüzmeye gitmek istiyorum
I am alittle tired, let me have a break 
I hope it is helpful... Kolay gelsin.
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