Does "married adults living with parents in parents' house" count as breaching the third precept?

To my knowledge, there are no teachings in the suttas that refer to sex outside of marriage as part of the Buddhist path. Every teaching about sex I have read is referred to in the context of marriage (e.g. AN 4.55; AN 4.53). Any sex outside of marriage is obviously motivated solely by lust (rather than mostly by compassion), which is unwholesome according to the suttas (MN 9, which states lust is the root of the unwholesome). Therefore, it is quite logical that any sex outside of marriage is a volition of the precept because it leads to hungry ghost, animal (AN 2.9) & hell realms (DN 31). Do we think a person that develops a habit towards unmarried uncommitted sex won't become a hungry ghost; similar to how men (who for some reason post on Buddhist chat sites) are often addicted to p**nography?

DN 31 says parents show compassion & protection (security & safety) towards their children by arranging a suitable marriage. This is the meaning of "protected by parents"; that parents protect their children from becoming hungry ghosts & bringing shame upon the integrity of the family. Thus, that the children are married means they have been protected by their parents, regardless of where they live. For example, in the time of the Buddha, generally the married children lived in the house of the husband's parents. DN 31 says:

In five ways, young householder, a child should minister to his parents as the East:

(i) Having supported me I shall support them, (ii) I shall do their duties, (iii) I shall keep the family tradition, (iv) I shall make myself worthy of my inheritance, (v) furthermore I shall offer alms in honor of my departed relatives.

In five ways, young householder, the parents thus ministered to as the East by their children, show their compassion:

(i) they restrain them from evil, (ii) they encourage them to do good, (iii) they train them for a profession, (iv) they arrange a suitable marriage, (v) at the proper time they hand over their inheritance to them.

In these five ways do children minister to their parents as the East and the parents show their compassion to their children. Thus is the East covered by them and made safe and secure.

Didn't Siddhārtha Gautama live in his father's palace after he married (and before he went forth)?

But I haven't heard a suggestion that that was immoral (only that it was impermanent and not ultimately-satisfying).

It seems to me obvious what "protected" means. For example, in contemporary Western society when my girlfriend and I started "dating" each other as teenagers, that was with our parents' permission ... it's for example when you're living with your parents, and when you're going to be "out" you tell your parents where you're going, and who with, and what time you're going to be back, and who will be driving, and the parents can say "yes" or "no" or set conditions.

Also I guess that when you're married and living with your parents, parents have already said "yes".

Also I guess that "living with parents after marriage" is pretty normal, not modern -- maybe in a new house on the same land. I'd guess that rather it's the nuclear family that's relatively modern (and not altogether a good thing).

Once you become married, you are the guardian of your partner. So you do not break the 3rd precept regardless of where you live. Parents continue to support you out of the goodness of their hearts. It does not make them your guardians once you become adults. They can kick you out at any time and be in the right.

I am confident that a married couple who live with their parents are not in violation of the precept against sexual misconduct. If anything the question would apply to the marriage decision (asking parents for consent), but certainly not sexual activity that happens after the marriage.

IMHO the point is that you need consent before having sex, and in the case of young people, you should not treat their own consent as acceptable because they are too young to decide, so any time you aren't sure, their parents should be involved in the decision. Honestly that sounds horrible either way, but we can imagine young people getting married and how the consent of parents would often be a factor in that union not being misconduct, especially in an ancient society.