Hello Lindley!
I am a single parent like you are, and I have found out that Walt Disney World is a great place to take your children on vacation as a single parent.
As far as riding rides with your two children, most of the rides in Walt Disney World have bench-style seating and can accommodate an adult and two children. For example, you can easily fit an adult and two small children on
Peter Pan's Flight or the Doom Buggies in
Haunted Mansion. For the rides that have individual seating, like the roller coasters, you could have your two children sit in front of you, and then you sit directly behind them in the same ride vehicle or the vehicle behind them. Another example is
Space Mountain; each shuttle has three individual seats in a row so that you can sit behind your sons in the same shuttle. You can always let the Cast Member, who is running the ride, know that you are a Single Parent and want to be seated as close to your children as possible. Cast Members are very accommodating to this kind of request, according to my experience. There are also a lot of family restrooms in the Parks where you all can go in together to avoid being separated when using the facilities.
I hope you have a magical trip with your children at Walt Disney World!
Marc L.