I'm presuming you're joing the Reg F, so my response will based on that premise.
Your trg takes precedence over everything else, full stop. That said, if you are between crses or are completed your trg by that pt in time, you MAY be granted lve. This doesn't mean you WILL be granted lve, but it is something that your CO or OC can consider, just like for any other soldier.
If your sister resides in the same location as your next of kin (if you are single and don't have kids, your NOK is Mom and Dad), than you may be eligible for Lve Travel Assistance (LTA) that will offset some of the cost of travelling "home" as defined under CBI 209.50.
The long and short of it is, if you are in trg (Recruit or Trades), don't bank on getting lve. If you are between crses or have reported in to your new unit after Trades Training, there is the possibility of being granted lve. But, if you are in this for the long haul, get used to missing birthdays, anniversaries, weddings, deaths, and all sorts of family occasions.
That said, best of luck on your courses and congratulations to your sister. Cheers.