From what I've seen, a Canadian tourist visa is possible even in seemingly very difficult circumstances (even if common "Internet wisdom" suggests otherwise). The key is (1) honesty and (2) building a strong case. Without knowing the details of your case, it is impossible to give specific advice, but here are some things that have helped me in the past when I was assisting with some very difficult applications:
- Open up, completely. Be completely up-front and honest about your situation. With many people who try to hide their real circumstances, this can really make your application stand out, and shows you're someone who respects immigration law.
- Make sure your application is well-organized, and that everything is clearly written (use proper English, good grammar, etc). Each section, if it has multiple documents, should contain a short (1 paragraph) summary page at the beginning, saying what these documents are, and what do they mean (why are you including them, what do they prove). Don't be afraid to highlight relevant portions of any complex documents. Pay attention to details. Make it look professional.
- List of required documents in the CIC checklist does not include a lot of documents that are useful to show ties to the home country (proof of relationship to family back home, proof of property ownership, etc). Don't be afraid to be creative and include these.
- The invitation letter is presumably read very carefully by immigration agents, and so it a great place to summarize your case. "I am inviting X and Y for a short visit only. They will leave Canada on Z date. Please consider the following points: ....". List as many good points as you can think of that show they're going to return.
- Back up the points with evidence. If any evidence relates to you (the inviter), add it as an appendix to the invitation letter. If any evidence relates to the people being invited (e.g. proof that sister is in university), refer to the relevant part of the application and attach it there. Weak evidence is better than no evidence at all.
- Finances don't matter too much for a short visit, but keep the following in mind: (1) The trip shouldn't "break the bank" for the people being invited - the expenses should not completely drain their life savings (it's hard to believe that someone will drain their entire life savings for one trip); (2) The trip should be easy spending money for you (the inviter). Say explicitly that you're willing to cover all expenses for people being invited, attach a tax document or a few paystubs, but no need to go into crazy amount of detail on your finances if it's just a few-week trip. (3) Take care of as many expenses as possible up-front. Say that you already bought airline tickets (attach proof) and health insurance (attach proof) so there won't be unexpected medical expenses, and that you're inviting them to live with you (so no accommodation expenses). The only thing left is food and tourist attractions (if any), and it's not a lot.
- It's good to show travel history - any is better than none
- It's good to show (if that's indeed the case) that the people being invited are educated professionals, for whom legal status matters. Obviously this is more difficult for a student.
- This may be controversial opinion, but I think it's good to show strong ties both at home and in Canada (as opposed to just showing strong ties at home). Someone who has strong ties in both places will want to travel back and forth, and that can't happen if you overstay
- Apply online if possible. Some of the bureaucratic requirements are less strict than for paper applications.
If application is denied, don't reapply without talking to a lawyer first.
Finally, do the mom and the sister have to visit at the same time? A whole-family reunion is nice, but from a visa perspective this may be easier as 2 separate trips. (Again, honest applications only - not "pretend that there are 2 trips", but really apply for a trip for 1 person, have her complete the trip and exit Canada, then apply for 2nd person).
