Japanese grammar "と", "たら" and "ば" different

Today I would like to discuss the 3 kinds of similar expressions in Japanese grammar- "と", "たら" and "ば".

"と" is used where the result is inevitable. It is a predictable event or an unavoidable fact. However, it can not be used when it comes to the speaker's wises, judgment, permission, hopes and requests.

ここを押せと、ドアが開きます。
ここを押せば、ドアが開きます。Ok
ここを押したら、ドアが開きます。Ok (Instead of “when you push”, here actually means “if you push”)

Hypothetical "たら"　is used in a conditional expression and indicates that an action or state will occur or appear when certain conditions have been met. It is not often used in newspaper and business environments because it is colloquial.

お金があったら、ニューヨークに行きたいです。
お金があれば、ニューヨークに行きたいです。Ok
お金があると、ニューヨークに行きたいです。x

Conditional "ば" is used to describe the environments needed for the certain event to manifest itself.

痛ければ、また来て下さい。
痛かったら、また来て下さい。Ok
痛いと、また来て下さい。x

More examples:

When I have time, I will bring kids to Hokkaido. (Undetermined and uncertain)
時間があれば、子ともを北海道に連れて行く。
When I have time, I will bring kids to Hokkaido. (Determined but uncertain)
時間があったら、こともを北海道に連れて行く。
I will bring kids to Hokkaido on summer break. (Determined and certain)
夏休みになると、子ともを北海道に連れて行く。