Did you have that tree planted? If so, have you considered contacting the nursery (the owner) to see if they are willing to do anything. You said that you had had the tree for only a couple of years, and that tree has had problems for a while. Sure, the tree is "out of warranty", but that doesn't mean that the nursery wouldn't be willing to work with you, and possibly considerably. If you planted the tree, or were there when it was planted, review the page linked below and compare what actually happened to what should have happened. As for getting someone to remove the tree and plant a new one, are you physically able to do that kind of thing, or do you have someone (family, neighbor, friend, etc) that is? With a small chainsaw (or even a good sharp pruning saw), a shovel, and an ax or mattock, the job wouldn't take very long at all. I would have it out and gone in about 15 minutes. Here is a link that might be useful: Planting a Tree or Shrub

How should I get rid of it? Also, it is appearing on the stems as well, if that makes a difference. My plant is looking rather unhealthy and is not showing much new growth.

Yep, powdery mildew and Liriodendron is fairly susceptible to tbis disease if the conditions are right. It tends to show up when temperatures begin to cool down, but the air is still humid. Warm days and cool nights are perfect for PM. This fungus does not need sitting water on the leaves in order to germinate, contrary to what many people believe....just humidity. As a matter of fact, spraying the foliage with plain water can be the simplest control, if caught early enough. Water kills PM spores. That's all I've ever used, as long as I spot it soon enough. At this time, don't worry about it; your tree is about to lose its leaves for the winter. I would absolutely treat the bare twigs with horticultural oil in the spring...just before the swollen buds begin to break. The potting medium must be one that is very porous, fast draining. Woody plants do best when grown in a bark based mix. The typical houseplant medium is not the best option for a woody plant. The location should be sunny and in an area of good air circulation. Avoid excess fertilization. There are many good options for prevention......plain water sprays, insecticidal soap, and neem are great preventative solutions. Some people recommend milk sprays or baking soda but be sure to research the mixing rates. Should you not be able to keep it rinsed away and infection occurs, Neem oil can cure a mild infection. Lots and lots of good information about this disease on line. Do some reading and you'll feel more confidant. It's not a mildew, per se, but a true fungal disorder. In ground trees can get it, too, if the conditions are right. PM spores travel in the wind. Check around to see if there are any other infected tulip poplars around just out of curiosity.

It's a scale infestation and a pretty severe one at that. Mulberries are prone to various types of scale, which are prolific, sucking insects that deplete plant vigor by feeding on internal fluids and juices. This looks like white peach scale (Pseudaulacaspis pentagona, aka mulberry scale). Control is difficult as the scale is armored so relatively immune to contact pesticides unless very carefully timed. A systemic may be your best bet but even they are only moderately effective and you may need repeat applications. You may want to check with your county extension service for their recommendations. And this is an extension fact sheet discussing the scale: white peach scale.