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Crossblooded clearly states:
At 1st, 3rd, 9th, 15th, and 20th levels, a crossblooded sorcerer gains one of the two new bloodline powers available to her at that level. She may instead select a lower-level bloodline power she did not choose in place of one of these higher-level powers.
Since you may only have one, if Tattooed Sorcerer replaces that, you do not get one.

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They can't be combined anyway, since they both alter the first level bloodline power class feature.
This has never been officially ruled on anywhere anywhere, and considering the way the Qinggong monk archetype works, it would seem that the Crossblooded would be similarly applied. Crossblooded lets you pick either or between two bloodlines, but anything replaced by another archetype takes precedence.
So like Errant pointed out, Crossblooded lets you pick either or at first level, however, Tattooed Sorcerer overrides that.

Lacdannan |

Maybe it is not explicitly stated that an archetype that changes a class feature and one that replaces the same feature do not stack, but it certainly is commonly accepted (although I thought it was written somewhere, /shrug). So do ask the GM nicely.
That said, I'd allow it. But I'm more liberal of a GM when it comes to these sorts of things.