I am not a single parent, but many of my trips have been as either a group of 3 or a group of 5. It's a lot less of an issue at Disney then you might think. A few thoughts:
Lodging: this one can be a bit of a pain. Your cheapest on-site option, would be a room at either Port Orleans Riverside or Caribbean Beach as they have a Murphy Bed that one of the children could sleep on. We were fine with this when the kids were younger, but it can get a bit cramped. A suite at All Star Music would be next cheapest and give you more room. But, the value resorts don't appeal to everyone. You could also fit in most deluxes, a suite at Art of Animation, or two rooms. Some people also rent dvc points, but I have no experience with that. Be aware that if you opt for two rooms, connecting rooms are not guaranteed. You will be told they are, but there are many reports of those who have not gotten them. We always have, but there is no way to know.
Dining: this one really isn't an issue. It can be a little harder to get the reservation in the first place, though. If you are not sure if you will have 4 or 5, book for 5. It's fine to show up with one less, but you can't always add on. As a party of 5, we are usually seated at round tables, half booths, or tables for 6. When the kids were little, we were also occasionally given a table for 4 with chair pulled up.
Rides: the overwhelming majority will fit 3 across even if they don't appear to. All your children are old enough to ride without an adult, so on those where you need to split up, you would be okay unless you have multiple timid children. Rides where you would need to split up:
7 Dwarves Mine Train, Goofy's Barnstormer, Buzz Lightyear, Speedway, Astro Orbiter and Dumbo (3 can fit on these last three with young children, but your crew is probably too big)
Expedition Everest, Rock n Roller Coaster, Toy Story Mania
Keep in mind that on most of these you would be in the same car as the children or right in front of/ behind them. Let me know if you have questions about any specific ride.
HTH