You have several options. You could take the Orlando Lynx bus system from the TTC. That would mean getting to MK, then taking the monorail over to the TTC. Then it's onto the bus, pay $1.50 pp, each way. Tell the driver you want to go to SeaWorld and you will get dropped at the parking lot entrance. It works fine, I've done it before. But.....
If you want to do it nicely, and since your mom is going, I would suggest getting a towncar to take you and bring you back. It would run about $60 r/t. You get a nice towncar, individual service. You will get picked up at your resort, and dropped at the gate to SW. You return when you want to rather than worry about a bus schedule, and then get dropped off at your resort. You should plan on a tip as well...so the total would come to about $72. But it sure is a nice way to go...especially with your mom and your little one.