It depends on us to make things work better between our children. It is a difficult task but the results are the most important part of it.
Children between 1 and 2 still don't get the difference between "mine" and "yours". The concept of sharing is new for them, and they want everything. At the same ages, it is impossible for you to explain why to is it good to share things with his sister/brother . I think nothing it's impossible. The problem is we do not have the endurance to do it, and, sometimes, time is our enemy. But things can work out.
Love is the key
Usually, the little ones do not love their new-born brothers/sister from the beginning. They feel or are pushed for doing it, and this is wrong. And even if they love them, this feeling is mixed with the anxiety that the baby brother or sister could take their place and they would be abandoned. Sometimes, these feelings are so extreme, that they could heart the baby on the side. This attitude is normal as long as you manage it, and help the older child to go through the mixture of feelings and acting.Problems between sisters/brothers
When they grow older, they could argue for everything, for a toy, for their loving parents, for books, pencils and every little thing that seems insignificant to us. My little girls, for example, don't want to share me, their mother. When I'm giving hugs to one of them, the other comes into my arms, too, and says: "Mommy is mine" and the other one says the same thing (even if she is 2), and they keep saying it non-stop until I start explaining them (especially to the older one who is six and is supposed to understand it better, although she is still a child, too) how things should work between sisters, how they should support one each other, and how mommy loves them both, with no differences. Sometimes it works, sometimes not, but I know that if I insist upon it, one day I'll see the results. The harmony between two children is different, and I see that, in most cases, children of the same sex argue more; and this is because they have common activities, they have to share specific toys, and, there's an endless competition between them.
Finally, you have to explain to your children what attitude is normal or not, and, most of all, to remind them every time how loved they are. Supporting them, giving them approbation, hugs and positive attention is a good method to reassure them that they are still special to you, and, on the contrary, if you get angry and yell at them, you'll get the things worsen.