The Kaytee Crittertrails aren't seen as good cages really - even with add ons the floor area is much too small - and yes tubes are a problem as they do block them up and dwarf hamsters aren't that good at climbing them sometimes. Looking at it the levels are a bit of a fall risk as well.
They do much better with one area of floor space at least 75cm by 45cm and that space filled with lots of substrate and floor toys. A short plastic tube run is fine as a floor toy but they're not good as access.
I'm guessing you're in the US? This is a good cage for a dwarf hamster. It's the same size as the duna multy. You'd need to take the wood items out as they're too big and meant for a rabbit! It costs $60. Some people use a glass tank or a bin cage as well. Smaller areas connected don't let them enjoy the natural behaviours - I think your dwarfie would really enjoy a new cage if the set up suits her better.
Something like the above with at least 4" deep substrate and a good sized house/nesting box plus floor toys would probably make her much happier
Things like toilet roll tubes, lots of hidey places (a tissue box is ok or a coconut hide). The main thing though is a good house or nesting box that is open underneath and sat on top of the substrate - so they can have normal behaviours like burying hoards under the nest and burrowng down. Some even like to dig their own tunnels in the substrate.
It also means you don't need to keep cleaning her out as that stresses them if its too often. With deeper substrate you can spot clean mainly and when they can have normal behaviours, they tend to be quite clean little things and pee in a sand bath and refurbish their nests and keep them clean.
tamburino
When you move them into something like that their little personalities really come out and they almost smile and start having normal hamstery behaviours. Having said that a move needs doing carefully as its a big change. Ideally let her play in the new cage the day before with some substrate and a couple of toys. Then move her over next day after setting up the new cage so you don't need to adjust anything for a couple of weeks. Normally it's advised to keep the layout similar but with the current cage type that won't be possible. But the main thing is don't clean anything when moving it over (any toys, house wheel etc) so they smell familiar and she settles in. If you need all new to fit in the new cage - eg a new house and wheel etc then just add a couple of things that are familiar from her old cage - eg a short run of the existing tubes as a floor toy eg. By a short run I mean just a few inches like a toilet roll tube - anything longer she may nest and pee in again. And her existing food bowl etc.
However cardboard is your friend - egg boxes, tissue boxes, cardboard tubes - they love anything like that and they're safe to chew on as well and easy to replace if they get peed in. A sand bath would be a good idea to add as well. Any kind of dish would do - eg a small pyrex casserole dish sunk into the substrate - some people use a salt pig or cookie jar as long as its something they can get in and out of easily. And put chinchilla bathing sand in it (must be sand not dust). They enjoy that for grooming and some will use it as a toilet so it helps keep the cage clean.