Looking at the map (and basing it on my own experience of only booking standard rooms), I think there is a very good chance that the first "box" on each trail coming out from the lobby is a standard room, at least for the lower (three and below) floors. Our first visit we were in the very beginning of the Kudu trail (about the third room in), on the second floor. While we had views of the animals, they were somewhat "obstructed" by some of the pens underneath (not a problem and we were THRILLED). I suspect the same will occur on the pool side of the hotel - the first "box" on those two trails will have pretty bad "pool views" depending on the floor, so they may be classified as standard rooms. Our other stays we've been on the third floor, either on Kudu or Zebra trails, further down the hallways but always close to one of the corners (which are considered to have "obstructed" views - and again we were always THRILLED.
This is why I have suggested that you "downgrade" - because I think it may ultimately help you get closer to the lobby, which is what it sounds like you would prefer. Again, I'm drawing conclusions based on my own experiences and the rooms I've had.
To give you a size perspective, I just looked at the room numbers on the map you posted - each "box" has about 16 rooms (per floor) which means only 8 rooms long before there is a viewing Windows and another section of about 16 rooms (so 8 long). So if you keep the pool view room, you can already determine that your worst case scenario in terms of walking will be that you must go to the back end of the lobby, go down two "boxes" on the Zebra trail, and maybe have to then turn right and go all the way to the end of that hallway. It wouldn't be the end of the world, and on the plus side, if you want to go to the wading pool, you'd be near the elevator that lets out right by the wading pool. So if you want to have a better shot (i.e., have a larger pool of rooms available near the lobby for them to attribute to you), you may want to consider downgrading.
If the "worst case scenario" walk is something that you're ok with, then stick with what you have and make it very clear that what is most important for you will be the proximity of your room with that of the other family in your traveling party. This point is very important - I always travel with my sister and her husband, as well as my own child. We live very far apart and see each other infrequently, so we have always requested rooms nearby. This has always been granted except for the last trip - we did on-line check in and indicated an early arrival. Reservations interpreted having a room ready at arrival was more important than close together, so we were put on two different floors. At the front desk (thanks Bradley you are awesome!) they were able to change this for us, but it required my sister and her husband to move all their stuff that they had already started unpacking. So just make sure that being together is noted as a higher priority than any other request.