always comes up as invalid position

[ichabod801]

If I set Row1 = ['-', '-'], I have no problems with the code. Of course, that's because it's not really doing anything, is it? It gets the input, starts the inputloop, and calls itself, which gets the input, starts the input loop, and calls itself, and so on until you get a RecursionError.

Perhaps that is being masked by your overly broad except statement. Except statements should be as narrow as possible, in this case only caching ValueError.

Regardless of the problems of using a global variable like Row1 (pass it as a parameter to the function instead), this should be a loop:

def qinput(Row1):
    inputloop = True
    while inputloop:
        try:
            Pinput = int(input("Where would you like to go?: "))
        except ValueError:
            print('Integers only please.')
            continue
        if Pinput == 1 and Row1[0] == "-": #checks if the position is free
            Row1[0] = " "
            inputloop = False
        elif Pinput == 2 and Row1[1] == "-":
            Row1[1] = " "
            inputloop = False
        else:
            print("invalid position - already taken!")
    return Pinput

And if the existence of Row1 implies the existence of Row2 and maybe Row3, I would suggest putting them in a list.