A new baby girl (her sister) obviously attracts attention from the parents, thus comes to the "competition of attention" she talks about in the second panel. She "removed" her to keep the attention on her ^^
People keep saying that on the twogag site aswell, but "I need solve this" is a correct sentence. It's normally slang, but it's also correct in normal use. Don't worry, if there's any comic artist that knows what he/she's doing, it's him/her. You can tell that by the complexity of some of her/his jokes.
It is? Then I guess I'll have to apologize (I'm just one of those people that like to point things out). I just thought it sounded funny when I read it without the "to". Anyways, thank you for telling me in a nice way!