You might be able to claim moving expenses, However, since your family is still in Canada, and you return home on the weekends, the CRA might not consider you as having moved.
Expenses like rent and travel costs can only be claimed if you have a T2200 from your employer stating that you were required by them to incur these expenses.
Child support payments can't be claimed, and neither are any payments that you send to your spouse. However you might be able to claim the spousal amount if your spouse has little or no income. You or your spouse might also be able to claim child care expenses, if you have to pay for someone to watch them while you work.
