I am also 5'9" pooh sized. You will be fine!
I have riden everything except the swings at DCA (which are currently closed and being redone to Silly Symphony Swings). I have also not tried the Mailiboomer, or the Golden Zehper, both also in DCA.
I have a little space issue on Space Mtn (space issue, get it!

), but that's because my legs are long and they touch the back of the seat in front of me. It's a lot easier to get out of than the one at WDW with that stupid bar right in the middle and you sit so low ... but that's another story.
The only thing with Space is there is some sort of total car weight restriction ... I don't know what it is, but if the CM telling you which row to get in doesn't pay attention, someone in your car may have to hop out and into another car. I have been on it too many times to count and it's only happened once. Both cars were full of adults (total of 12 adults). It was no big deal, here's what happened. The car pulled forward for the lap bar check, then the CM asked DH and I if we'd switch to a different car. They "beeped" us over to where they do the HA loading. We hopped out, that car beeped back over, then took off with our seats empty. They loaded us and some other people transfering from a wheel chair and their party into another car and we were off. No one said "hey get those fat people outta that car!" or made us in any way feel like we were being singled out. It was very casual, and if I remember correctly, I had to ask if something was wrong. It's quite common for the cars to be switched on the track for the HA loading. You'll probably hear the "beeping" that happens when the cars are moved around on the tracks several times while waiting. So hardly anyone pays attention to it anway. But like I said out of all the times I have riden this ride, it's only happened once.
DH and I have even riden Peter Pan together (he's pooh sized too) and it was fine. I was little worried the first time because I didn't konw what to expect, but all was fine. You could do one kid with each parent onthat ride.
As others have said, check out the photos of the ride vehicles before you go. Worst case, you could always take the "chicken exit" out of any ride at the last min if you got too worried, but I say give it a try!