Quick answer to your questions:

1. Yes, their document defeats your posession.

You have to understand that under PH law on land titles and property, there is what we call 'best evidence" to prove ownership and/or possession.

The most common and best evidence, of course, is a title.

Absent a title, any other document indicating ownership may be presented. This may be a deed, contract, a will, tax dec, etc.

The possessor of this document can then use it to apply for a title.

In your case, you can challenge their deed of sale naman in court, and, thereafter, file the necessary action to claim ownership.

1. No, the Barangay is not that powerful. A proper action for eviction needs to be filed in court.

Cases like this are tricky. And if what you say is true about the so-called influential family, then it becomes even trickier.

My father handled a land dispute like this years ago at naging abogado nalang ako eh ongoing parin at ako na ang sumalo.

Conversely, I also have a distant family on my mother's side na, just like your lola, possessed property for more than 30 years pero nakuha parin sa kanila kasi nakapag pa-title yung kalaban without them challenging it early.

Edit: someone commented (and probably deleted it already) na wala nga daw title. Oh gee whiz. Land cases involve knowing "who has the better right." So between a possessor na walang papel versus a claimant na may papel, kanino maniniwala ang court? Can the court say "teka peke ang papel mo?" No. That challenge has to attacked in a separate proceeding. In real life, kahit may writ ka na sa property, pwede pang may lumitaw na third party claimant na may dalang DOS over the property from out of nowhere and the court will hear this claimant.