Re: Bear with me........
I wouldn't depend on your Uncle to help with your current situation. As someone said earlier, a reluctant "Yes" is as good as a "No"..
If your uncle cared about his Sister as much as you care for your Mum, years ago he would have offered a helping hand, rather than only offering when you asked. I don't think you can rely on him and if you up-sticks and move around the World, I think you will find that things will be harder than they were before.
I had a friend whose family did something similar. Her family asked a relative in the US for help with her Mum who was ill. They said all the right things and made all the right promises but when they landed there, nothing had been sorted for them. No accomodation, schools/education for her siblings, work for her Dad (that was promised by one of the relatives), nothing. They were all cramped in their relatives house and the relatives began to resent them due to the lack of space. It took years for her family to even begin to start finding their feet and throughout that time my friend had to make a lot of sacrifices. Even now, years later, things are still a struggle and all the promises they made have yet to be fulfilled.
I would talk with your Mum and ask her what she wants. If you do decide to move to the US, then I would plan everything and arrange everything before you begin to think about packing up abd booking tickets. Get a property first. Would you buy or rent? go on the internet, register with some letting agents. Find a good one and build a rapport with them. ask them to send you pics of properties, areas, measurements of rooms, etc etc. Keep in constant contact with them. Ask them to let you know as soon as a property comes on the rental market. Explaion your situation to them. when you find a property you like the look of, with nice area, good transport links, close to work (you need to think of all these things) then ask them to draw up a tenanncy agreement and have them fax it over so you can sign and fax back. At the same time look for jobs. Update your CV, email around the CV to companies in the area you want to live in. Offer yourself up for phone interviews and register with employment agencies.
what about "green cards" and social securoty numbers? I don't know how all this works but you do you need all this before you can even rent property, work, get healthcare? Look into everything, do your research and plan everything BEFORE. DO NOT rely on your Uncle tyo do it. Chances are if he did do something it, it would be a half-hearted effort. He would probably rent your out the cheapest, smallest property because he couldnt be bothered to look for anything else...
If you do decide to do this, be prepared!! Good luck!!