I have a sidekick 3 in the US, and I went through loads of trouble trying to find a way to bring mine to the UK. Unfortunately, you can't just have your mom send it to you and stick in a t-mobile UK sim card. I called T-Mobile UK and US and asked them both, and they are not the same network. Because of this, it's just as if your phone was from Sprint and you were trying to use a Cingular sim card. You have to get the phone unlocked.
What's even more unfortunate is the fact that you cannot unlock a Sidekick. Because the phone connects to the Danger servers for most of its applications (ie, using the internet, messengers, and texting, etc etc), some of the features would "break" if you unlocked it. They would not give me any information other than "Sidekick phones cannot be unlocked". In addition to that, if you try to google "unlock sidekick" or some other combo, you most often get results from message boards where person after person post something about getting a sidekick unlocked and loads of people telling them you can't, etc.
So unfortunately, you can't use one in the UK if it was originally a US phone. I wish it was possible, because I'd have mine with me here too.