Creating a simple 52-card data structure for Blackjack in Python
One thing that catches my eye:

Default list argument.

There is a bit of a footgun hiding in this method:

def __init__(self, card=[], card2=[], score=0):
    self.card = card
    self.card2 = card2
    self.score = score


Default arguments are only created once, when the method is defined.  The end result is that all Hands using default arguments will share the same lists. Observe:

&gt;&gt;&gt; first = Hand()
&gt;&gt;&gt; first.card
[]
&gt;&gt;&gt; second = Hand()
&gt;&gt;&gt; second.card.append(1)
&gt;&gt;&gt; first.card
[1]


I mention this not because it currently causes problems in the code (it does not; card and card1 are never modified in-place), but because it is a problem you are bound to run into in the near future (or perhaps already have!).

There are a couple ways to get around this. 

A good placeholder value is usually None.  The following lists are created each time the function is run:

def __init__(self, card=None, card2=None, score=0):
    if card is None: card = []
    if card2 is None: card2 = []
    self.card = card
    self.card2 = card2
    self.score = score


If you immediately take a copy of any mutable objects then they are harmless:

def __init__(self, card=[], card2=[], score=0):
    self.card = list(card) # copies the input list
    self.card2 = list(card2)
    self.score = score


("mutable" objects are those that can be modified in-place; list, dict, and set are mutable.  int, tuple, and str are immutable, and they are safe to use anywhere)

But I feel the most important alternative is probably this:

Simply require the cards to be passed in.

def __init__(self, card, card2, score=0):
    self.card = card
    self.card2 = card2
    self.score = score


Generating cards and remembering (i.e. storing) cards are two separate responsibilities.  It is clear (from the fact that playerScore and dealerScore both index into self.card[0]) that, in general, this class is expected to contain cards.  Therefore, a different one should generate them.

That said, it also has the dual responsibility of both tracking a score and making decisions based upon that score.  In fact, it would seem that these two are the only real reasons it needs to exist.  It feels more like the class is trying to be this:

class Player:
    def __init__(self):
        self.score = 0

    def playerScore(self, card):
        value = str(card)
        if value.isdigit():
            # yadda yadda yadda ...

    def dealerScore(self, card):
        value = str(card)
        if value.isdigit():
            # yadda yadda yadda ...


in which case we never even need to store the card in the class!

Duplicate logic 

playerScore and dealerScore duplicate some logic which can be factored out with a flag:

def addCardScore(self, card):
    value = str(card)
    if value.isdigit():
        self.score += int(value)
    elif value == "Ace":
        if self.playerType == 'player':
            self.playerAceValue()
        else:
            self.dealerAceValue()
    else:
        self.score += 10

def playerAceValue(self):
    aceChoice = input("Play ace as 11 or 1? ")
    while not aceChoice.isdigit():
        try:
            aceChoice = input("Play ace as 11 or 1? ")
        except TypeError:
            print("Invalid response.")
    if aceChoice == "11":
        self.score += 11
    else:
        self.score += 1

def dealerAceValue(self):
    if self.score &gt;= 11:
        self.score += 1
    else:
        self.score += 11

# ... somewhere else, not necessarily in a class ...
def playGame():
    player = Player('player')
    dealer = Player('dealer')
    while True:
        playerCard = drawCard()
        player.addCardScore(playerCard)

        dealerCard = drawCard()
        dealer.addCardScore(dealerCard)


This code has a new issue: looking at addCardScore, we see that two branches of the if modify self.score, but it is not immediately obvious that the middle branch (elif value == 'Ace') does the same.  Generally speaking, by rewriting the functions so that most of them simply return values instead of modifying members, it becomes generally easier to reason about when data is modified.  Here's an example version where only one function touches score:

def addCardScore(self, card):
    self.score += self.getCardScore(card)

def getCardScore(self, card):
    value = str(card)
    if value.isdigit():
        return int(value)
    elif value == "Ace":
        if self.playerType == 'player':
            return self.playerAceChoice()
        else:
            return self.dealerAceChoice()
    else:
        return 10

def playerAceChoice(self):
    aceChoice = input("Play ace as 11 or 1? ")
    while not aceChoice.isdigit():
        try:
            aceChoice = input("Play ace as 11 or 1? ")
        except TypeError:
            print("Invalid response.")
    if aceChoice == "11":
        return += 11
    else:
        return += 1

def dealerAceChoice(self):
    return 1 if self.score &gt;= 11 else 11