There are plenty of sites out there for finding remote work.
Part time, and remote will be harder but not impossible.
There are two big reasons why you don't see more remote and more part time. Training and collaboration.
Lets assume that your talking about programing/engineering and that your a senior developer. You already know how to do your job (write code) but what you don't understand yet is the domain your about to go to work in. There is a fixed cost where your "ramping up", learning about how the business works, the nomenclature used to describe behavior, and functionality. Unless you have been in an industry for a while, this will all be new to you. During your first few weeks/months the company is paying a tax for you to learn, not only their environment but the particulars of what they do.
Once your past that first stage and part of the team, what happens then? If your not present (your day off) and someone needs advice (integration, production support ... ) on something you have built what do they do? Are they going to read through your code (Yes they can, most people don't know how or don't have the patience), are they going to wait or be stuck till you get back? People being "present" at the same time and in the same location makes these sort of issues less likely, it keeps productivity high.
This work does exist. The trick is to be a solid developer AND a domain expert. Your then going to have a set of skills that lets you target specific companies who will need your skill set, and be able to set your terms. At that point however, your not going to be seeking "part time" you going to be charging flat rates per week for much larger sums of money. The pay won't be "steady" but the peeks and valleys will provide you more than your currently asking for.