My DH is Kenyan and used to be a safari guide at Cottars in the Mara.
Malerone is ok for children over 11kg (or something like that) so provided your 18 month old is heavy enough that should be ok. You'll all need Yellow Fever certs as well and I think typhoid, hep A one other I forget....
DH is saying the road into the Mara is not the best with small DC so you would need to fly in/out (charter flight probably from Wilson or there are 2 scheduled services/day depending on which lodge/camp you are looking at).
He also says it depends on if you are going in a family group ie. only you and your family on your game drives or if you will be with other people. Becuase you will need some flexibility with the times of the game drives and also your DC might have had enough after 1hr of sitting in a vehicle which is usually very open sided and not being able to get out etc!
Normal game drive times would be 6.30am-9am and then again in the afternoon 4-6.30pm roughly. If there are other people going on the game drives they will set the times - if you are in a high end camp / big enough group for 1 vehicle you may have some flexibility with this.
DH says it's rare to see children under 5 in the luxury camps - it's a v expensive trip and children under school age will not appreciate it hence not a lot of people bother. He does say local families with their own vehicles would be more common though than people bringing young DC from overseas so it must be do-able!
BUT seeing as you are already in the country it's not like you are making a special trip and a couple of days isn't too long... Perhaps you and DH could alternate who goes on the game drive and the other one stays in the camp with the kids?
Please bear in mind I really don't think any of the camps will be geared up for young children so you will have to bring some entertainment - if you are flying in/out you will be very limited with luggage.
If you can tell me which lodge/camp your brother is thinking of I can ask DH more. I would really suggest a lodge rather than a "camp" and would not recommend actual camping with such young DC in Africa.
Someone will now come along and say they do it all the time and it's fine 