Anissa,
I'm going to respond to both of your questions.:) Your neice first. She is two, and it is very normal for them to test their limits. You just need to be firm, yet loving, if she won't do what you say, or is mouthy, I would give 1 warning, and then it's off to time out. I have four children, my youngest is three, so we have a specific seat for time out.
Warning ~ She will son and cry and maybe scream, but you are the BOSS, you have to set the tone!
Now, your 8 month old, also at an age where she is testing her limits. Of course it's funny to hit mommy, look at that face she makes! lol But if she knew that it hurt, she probably wouldn't do it. What I used to do with my daughter when she did that, is I would take her hands, hold them with mine, and tell her, that hurts mommy, ouch! After a little while she got it. The trick is gently holding her hands, and making eye contact.
I hope this helps! I wish you the best, I know you have your hands full!
L.