Leaving all other mistakes aside, let's concentrate on the verb tense.

Generally speaking, the perfective aspect indicates completed actions and the imperfective indicates ongoing actions (incomplete or recurring). In this case, you are talking about a completed action: you moved and, as a result of that, you were in a new house, where the rest of the action happened (your brother did not like one of the rooms and so on). So you have to use the perfective aspect: mudamos rather than mudábamos.

As for the other verbs, you have to use the perfective too for the third verb (took), which is an instantaneous action and, therefore, completed as soon as it is started. But the second verb (want) is tricky; you can consider that it is also an instanteneous action (there were two rooms, your brother said no to one of them, and then you took it), or an ongoing action (your brother had been complaining about that room for some time and at some point you decided to take it). So you can actually use the perfective or the imperfective.

Putting all together, and fixing the translation a bit, you have these two choices:

1. Mi habitación es rosa. Cuando nos mudamos, mi hermano no quiso la habitación rosa, así que la tomé yo.
2. Mi habitación es rosa. Cuando nos mudamos, mi hermano no quería la habitación rosa, así que la tomé yo.

Leaving all other mistakes aside, let's concentrate on the verb tense.

Generally speaking, the perfective aspect indicates completed actions and the imperfective indicates ongoing actions (incomplete or recurring). In this case, you are talking about a completed action: you moved and, as a result of that, you were in a new house, where the rest of the action happened (your brother did not like one of the rooms and so on). So you have to use the perfective aspect: mudamos rather than mudábamos.

As for the other verbs, you have to use the perfective too for the third verb (took), which is an instantaneous action and, therefore, completed as soon as it is started. But the second verb (want) is tricky; you can consider that it is also an instantaneous action (there were two rooms, your brother said no to one of them, and then you took it), or an ongoing action (your brother had been complaining about that room for some time and at some point you decided to take it). So you can actually use the perfective or the imperfective.

Putting all together, and fixing the translation a bit, you have these two choices:

1. Mi habitación es rosa. Cuando nos mudamos, mi hermano no quiso la habitación rosa, así que la tomé yo.
2. Mi habitación es rosa. Cuando nos mudamos, mi hermano no quería la habitación rosa, así que la tomé yo.