"That" is a word which is used for many different purposes. It fills a lot of different grammatical roles. Attempting to use such a broad rule as "use a comma after 'that'" will result in very poor sounding and looking sentences. In fact, I'm pretty sure (this is just an estimate) that the majority of uses of the word 'that' will not involve a comma -- like the one in this sentence.
There's a lot of errors in your sentence, unfortunately. I'll start with the usage of commas in it, so you can skip the parts that aren't related to your question specifically, if you choose.
Yes the most important thing for me is that you live happy that's it , with smiling face.
This thing matter to me a lot. Try last time , try as much as you can.
The first comma between "it" and "with" is not correct. "with [a] smiling face" is a prepositional phrase. There isn't any reason to separate it from the sentence with a comma. Your second comma, between "time" and "try", is also incorrect. This is known as a "comma splice," and it's a very common and very grievous error. Comma splices are made when the author uses a comma to "splice" two sentences or complete thoughts together.
Notice that you can write "Try [one] last time." and "Try as much as you can." as separate sentences. You need a conjunction to link these sentences together, or you'll make a grammatical error. The standard conjunctions (for, and, not, but, or, yet, so) don't work here, because of the nature of the two sentences; none of the conjunction words fit in this context. Fortunately, you can use a semicolon, just like I did in the last sentence. If you're really in doubt, you can probably use a semicolon whenever you would accidentally make a comma splice (just replace the comma with the semicolon). The semicolon definitely works in this situation.
Moving on to non-comma related errors, you may have noticed that I put words in brackets ("[]") when quoting you above. I was indicating that I added that word into your statement because it would have been incorrect otherwise. You seem to have a problem with missing words. These are the two phrases which need words added to them, or they won't be grammatically correct:
with a smiling face
Try one last time
You can also rewrite these phrases ("Try again for the last time"), but I was trying to change your sentence as little as possible. Now, I'll go through each of the 3 sentences.
Yes the most important thing for me is that you live happy that's it , with smiling face.
Yes should either be removed or separated somehow. It could be its own sentence, used as a reply on its own ("Yes. The most important...").
Live happy should be live happily. "Happy"/"Happily" is describing the verb "live." You must use adverbs if you are going to describe a verb, or an adjective, or another adverb. "Happy" is an adjective, and therefore can only be used to describe nouns.
That's it, like "yes" at the start of the sentence, must be separated with some form of punctuation or transition. I'm not sure what point you're trying to get across exactly when you say "that's it," but I assume it's something along the lines of "all I care about is that you live a happy life." If that's the case, you should consider rewriting the sentence to reflect that. You can also have "that's it" be a sentence on its own; "That is it." is a complete sentence.
This thing matter to me a lot.
This thing is redundant. You have already described and established the context. If you had said "this," we would have understood that you were talking about "living happily," because there isn't anything else for it to refer to. Qualifying "this" with a noun such as "thing" or "man" is usually used when talking face-to-face, with the help of body language, so you can differentiate one object from another by gesturing to it. "This" can be used as both a noun and an adjective.
Matter must be changed to "matters." In English, you must use the proper verb form depending on whether the subject is singular or plural. Most of the time, the singular form is simply the word as shown in the dictionary with an "s" added to the end. The subject ("thing") is singular.
Try [one] last time; try as much as you can.
I have already mentioned the comma splice and the missing word, so moving on from that... there isn't anything else wrong with this sentence that I can see.
This thing matter to me a lot.