The only complications that will occur will be in the birth of the second child, and that too if the second child is conceived soon after the birth of the first.
Let me explain.
Rh factor is an antigenic protein found on the surface of the RBCs of some individuals( rather, 'most individuals').
If the factor is present, the blood group is written with a positive(+) sign, and if it is absent, the negative sign(-) is used with the blood group. Therefore, in your example, Bob, Abraham and Abigail have the said factor on their RBCs whereas Alice does not.
As a matter of fact, our body has a mechanism because of which it produces antibodies against foreign antigens. Antibodies are simply substances released by our specialized cells to counter toxins and foreign antigens. These antibodies bind with the specific antigens (against which they are released) to render them harmless.
The fact is that these antibodies, once produced in our bodies, remain in the bloodstream for a certain interval of time, and there presence protects us from future infections by those antigens(This is the principle exploited in vaccination).
Let us relate this knowledge of antibodies and antigens to the Rh factor. Let's say that we make a blood transfusion from an Rh positive person(like Bob) to an Rh negative person( like Alice). Since for Alice, the Rh antigen is a foreign antigen(because it is naturally absent from her blood), she will get sensitized and develop antibodies against it. However, these antibodies will not attack the antigens immediately. They will come into action only if the antigens are again brought into the bloodstream, i.e. another transfusion is made sometime later. These antibodies will then bind to the RBCs carrying it, and result in agglutination, or clumping of RBCs. The clump of RBCs thus formed blocks the passage of blood to the heart, resulting in death.
So, if Alice and Bob conceive a child together for the first time, the fetus will be Rh positive(because if the factor is present in any one parent, it will also be found in the child), and it will sensitize the blood of the mother. At this point, if you know some basics of biology, you will think that since the blood of the mother and the fetus never comes in contact, the fetal blood should not be able to sensitize the mother's blood. If you think so, you are absolutely right! The placenta does not allow their blood to mix. However during the parturition, rupturing of placenta often occurs, causing just a small amount of the fetal blood to mix with that of the mother. Even this small amount is enough for the mother to be sensitized and develop antibodies against Rh factor.
Now, if the second child(who will also,obviously, be Rh positive) is conceived soon, there will be a problem. The placenta is permeable to antibodies, and as a result, the anibodies developed earlier will enter the fetus and cause agglutination in the fetal blood, leading to excessive anaemia or even death. This is called erythroblastosis fetalis, or hemolytic disease of the newborn(HDN)
Thus, you can see that Alice and Bob will have a problem with their 2nd child, whereas Abigail and Abraham will not, since they are both Rh positive and Abigail won't be sensitized.
FACT The Rh factor was first found, and named after, the common Rhesus monkey!!
