Translation:I think Ms. Tanaka will probably come to school.
"Probably will come to school"
"Will probably come to school"
"Will come probably to school"
The first two should be accepted where the last one probably shouldn't as far as I think. I'm not aware of any rule saying that we can only have "probably" between "will" and "come".
The first, "Mr(s) Tanaka will probably come to school", only expresses the estimated likelihood that (s)he'll come.
The second, "Mr(s) Tanaka probably will come to school", feels like there is some implied constrast. E.g. "(s)he will come, but 本田さん won't", or "at first (s)he wouldn't come, but now the situation has changed".
The rule is that the verb directly in front of と should always be in plain/informal form, and as V2Blast just said, there already is one, namely 来る. だ only shows up in constructions where the first clause would otherwise end in a noun or adjective. E.g. 犬だと思います ("I think it's a dog") or 花は紫だと思います ("I think the flowers are purple").
In different languages, sentences can have different word orders. If you keep the Japanese word order in a literal English translation, you end up with Yoda English. Instead, you have to look at the rest of the sentence, break it down into the right segments, and restructure to fit the language you're translating to.
For example: 田中さんは --> Mr/Mrs Tanaka, たぶん --> probably, 学校に来る --> come to school, と思います --> I think. In other words: "I think Mr/Mrs Tanaka will probably come to school."
The thing about this sentence is, Tanaka-san is probably a fellow student, so it is odd to translate the "-san" as "Mr.", since high school kids usually don't refer to each other as "Mr." and "Ms." If Tanaka were a teacher, he (or she) would be called "Tanaka-sensei". I think in this case, it's probably best to leave the "-san" as is in the translation.
Google Translate is often innacurate or lacking, especially for Japanese. たぶん basically means "not 100% certain", so it can be translated as both "maybe" and "probably". If you want to emphasize that the probability is high, then "おそらく" might be better. If you want to emphasize that the probability is not so high, then adding "かもしれない" to the end of the sentence will get the point across. If you are uncertain when the other person uses "たぶん" you can say, そのかくりつは？ which means "What is the probability of that?
I typed in "Mister Tanaka", and it told me it was wrong and gave me "Miss Tanaka" as a correction. (╯°□°）╯︵ ┻━┻ I still haven't been able to do one the placement tests without mistakes even for my natives language. The Japanese course is particularly flawed because Japanese grammar and sentence structure are so different from English.