Translation:It is not possible to get under that bridge alive.
Yeah... tricky. First of all, it's also correct to say "Pod ten most se není možné dostat živý" - here we have "se" in the second position, and I'd say it actually sounds better.
So far, you have seen sentences where "se" or "si" belongs to the main verb. This is a little different, as the reflexive verb "dostat se" is in the infinitive, it's not the main verb of the sentence. Here, the reflexive pronoun can stay attached to its verb, it's not so strongly pulled to the second position. As soon as it becomes the main verb, the second position is a must: "Dostaneme se pod ten most živí?", "Pod ten most se nedostaneme živí.", "Tam se živí nedostaneme."
In the future tense, the "bude" is auxiliary, therefore the verb itself is still the main verb (even though we use the infinitive), so what I wrote doesn't apply there, and you're remembering correctly. Basically, keep putting "se" in the second position. Even in this exercise, it would still be good there. Just notice that in longer structures, other positions may be possible as well.
And even when the reflexive verb is not the main verb and the main verb is something like moct (can), potřebovat (need), chtít (want), muset (must), "se" will still gravitate to the 2nd position: "Dnes se musím vyspat." (I need to have a good sleep today.), "Ještě se můžu dostat domů." (I can still get home.) - these would both sound wrong if we didn't apply the second position rule.
OK, I just thought of an example. Let's combine "přát si" - to wish for something (literally "to wish to oneself", as opposed to just "přát" which is used when you're wishing someone else something) with a se-reflexive verb, let's stick with "dostat se" - to get somewhere (as opposed to just "dostat" which means to get something).
If I want to say "Do you wish to get to the university?", I will say: "Přeješ si dostat se na vysokou školu?" - here the "se" will go AFTER the secondary verb simply for the reasons of euphony - "si se" sounds bad. But when I replace "přát si" with "chtít", it becomes the normal "Chceš se dostat...?" because nothing is preventing "se" from assuming its normal position.
We can also see that "si se" sounds bad whenever the auxiliary "jsi" meets with "se", such as "Chtěl jsi se dostat na vysokou školu" (You wanted to get to the university) - that is also pronounced /si se/ and it automatically contracts to "ses" (at least in good Czech). Similarly, "jsi si" contracts to "sis".
I believe that by "auxiliary" you mean "se" or "si". They are reflexive pronouns (like "myself" in English). The term auxiliary is used for helping verbs such as "do" in "do you want...?" or "will" in "I will go...". In Czech, auxiliary verbs are forms of "být" in the past tense: "Dělal jsem..." and the future imperfective: "Budu dělat..."
So if you mean "Does the reflexive pronoun always come before the second verb?" - I'm afraid I don't have a good answer, there is very little material on this topic, so I have to just try sentences in my head. And they have to be long and complicated sentences, otherwise "se" simply goes second. It is possible to find sentences where "se" appears even after the secondary verb, but in all those cases (that I can think of) it can also go before it and feels better there. There are sometimes complicated sentences where more "se"-words clash - there can be two reflexive verbs in one sentence, or one "se" can belong to the passive voice and another to a reflexive verb. "Se" is also used to mean "each other". Sometimes two of these different "se" merge into one, or they just appear in weird positions. Another "se" is the vocalized version of the preposition "s" - but that one doesn't cause any trouble because it's safely fixed in place.
A humorous but actually simple sentence is: Nesnese se se sestrou, it's funny to say out loud. It means "He and his sister can't stand each other" - the second "se" means "with", and the first "se" can be interpreted either as this "each other" bit or as a part of the reflexive verb "snést se" - to (mutually) get along with. If it wasn't mutual, i.e. he can't stand his sister, it would be "Nesnese/nesnáší svou sestru" - no reflexive there.