"After discussing plans for seaside vacation, Victoria realized that she likes the ocean more than Doug did."
"After discussing plans for seaside vacation, Victoria realized that she likes the ocean more than Doug does."
Your question involves the topic of backshift.
(Note: "preterite" is the same thing as a "past-tense verb form".)
ASSUMPTION: I'm assuming that, in your scene or situation, Victoria realizes that she likes the ocean more than Doug does. The rest of my post is working off this assumption.
The reason that version #1 is ungrammatical is that: once you decline to use a backshift preterite when it could be used, then you can no longer use a backshift preterite further on in the clause(s).
Both versions #1 and #2 declined to use any further possible backshift preterites when they both used the present-tense verb "likes". They could have used the backshift preterite "liked" here, because the superordinate clause itself is headed by the preterite "realized" which is enough to enable the use of backshift for the rest of the clause which includes its subordinate clauses.
The superordinate clause is headed by the verb "realized", which is a preterite (a past-tense verb form), and so, that means that the subordinate clause "[that she likes the ocean more than Doug does]" can now be (optionally) backshifted.
For version #a, the subordinate clause isn't backshifted. That is why the verbs "likes" and "does" are still in their original present-tense forms.
But for version #b, the subordinate clause is backshifted. And since the verb "liked" is a backshifted preterite, the option to use backshift is still available later on when the verb "does" is reached. Though, if the first verb "likes" is backshifted, then speakers will (almost) always also backshift the verb "does" -- that is, both get backshifted or neither does.
The problem with your original #1 version:
- "After discussing plans for seaside vacation, Victoria realized that she likes the ocean more than Doug did."
is that the last verb "does" was backshifted into "did", but the earlier verb "likes" was not backshifted. That is not allowed, not for the sense of meaning that you wanted for that sentence.
So, in summary, for your example it is usually the case that either both of those verbs are backshifted or neither are backshifted. (Your original version #2 has both not be backshifted.)
ASIDE: In today's modern fiction prose, when it uses past-tense narrative mode, it seems that writers tend to prefer to use backshifting for the subordinate clauses (e.g. version #b "that she liked the ocean more than Doug did").
NOTE: The preterite (a past-tense verb form) has three major uses: past time usage, modal remoteness usage, backshift usage. (Though, there are other uses too.)