What happens if all 3 teams end with same record?
I had understood that the winner of two tied wild-card teams was decided with a coin flip. Is that right?
Not exactly. Since the Dodgers and Padres are in the same division, they would play a one-game playoff to determine the division winner (NL West).
The winner would make the playoffs by virtue of winning the division.
The loser would miss the playoffs by virtue (or vice) of having a poorer winning percentage than the Phillies, since they would have the same number of wins but one more loss.
Thus in this scenario (Dodgers, Padres and Phillies all have the same record on the last day of the season), the Phillies would win the wild card in either case.
There are also plans if three teams tie for the division title, but none qualify for the wild card. They actually had these in place this year in case there was a three-way tie with St. Louis, Houston, and Cincinnati. It’s actually quite fiendishly clever:
The teams flip coins to determine who goes first. Then, the have the choice of three options:
A. A single playoff game, but it’s on the road.
B. Two playoff games, the first on the road, the second at home.
C. Two playoff games at home.
Thus, whoever picks (or is forced to pick) C would play B at home. If C wins, A comes to town. If B wins, they go home to face A.
Teams have to choose. If you get first pick, do you prefer to play one game to win it? Or would you rather play two games at home? Or doesn’t it matter and you choose B?
Whichever you pick, you could be second-guessed for ages. 
Is this true? I didn’t think the 1-game playoff would be counted in the final standings. The last two teams need to play another 1 game playoff to determine the wildcard spot.
You are correct. The Dodgers would play the Pads for the division and then the loser would play Philly for the wild card.
Any of these games would count as regular season games though so the player stats would count and the games would end up in the final standings.