HOW do I do this?

Like Valhalla360 stated, domicile can be difficult to establish and, as you apparently know, NY does not let go easily. If you don't plan on being in NY more that 180 days each year, there's nothing wrong with establishing domicile elsewhere. Keep in mind owning real estate, even in NY, does not by itself make one a resident at that location.

A good source is the Escapees site and forums, and they have a well-established mailing service for those who choose SD, TX, or FL. As a FL resident, I can tell you the state is well-prepared to handle non full-time residents, what with the big numbers of snowbirds and RV'ers. It might even be worth a trip to FL to sell the existing RV and purchase new in FL, and establish domicile at the same time.

This may help, While out of state

Because we won't be back in NY until mid december soonest. Need to register it somewhere and not sure if I can do it virtually in ny and with appointments necessary at motor vehicle...that could be difficult or impossible?

Maybe this won't work?

Are you selling your NY home? You can't just transfer the plates from your old rig to the new?
Also what are you trying to accomplish tax wise? Ny taxes vehicle once per owner,when you purchase. and our registration fees are actually quite reasonable compared to other states.
To sell your old oneyou need a trusted friend /relative or a consignment lot.

If going to domicile in NY, why get SD involved? Can likely get a temp tag to get to NY, for any inspections needed to title/tag it. Then do your sale in the state you know best.

I am fully aware that NY state, a high tax state won't give up easily...so for now NY will be our domicile...don't want them coming after me for $$$.

Can I register it in South dakota...with me driving said rv to south dakota and husband taking the new one and hang until we sell it? Sell it to a car lot? any other ideas how to move it quick? Before hand put it up for sale in michigan?

I hope I can get this to work.

Selling/Buying: Selling might be a challenge but now is probably the best time in years to do it on the road with sales thru the roof. Plan on stopping somewhere for a month or so because realistically, you will have to show it to potential buyers. Probably in Michigan, so you can transfer your stuff to the new RV or if you have a friend who can show it, put it in storage near them (and make sure they have a good understanding of how things work). It will still likely by a bit of a hassle doing paperwork remotely but certainly doable.

Domicile: Unfortunately, it's not fill out a form and you have a new domicile...you have to build up a case. With "normal" people, it's clear cut because everything is quickly transferred to their new state. Key items are they sell the old house and buy a new house. Likewise, their job moves from the old state to the new. License, registration, utilities, etc...all transfer to the new state. They wind up spending upwards of 90% of their time in their new state. It's all very obvious and clear cut.

As a full time traveler, you don't have several of those key data points, so you need to make sure as much as possible that what you can document that you aren't domiciling in NY.

If you will still be spending significant time in NY, you may have difficulty changing your domicile. They aren't dumb and if it's going to cost them tax/registration dollars, they will challenge it, if it's not clear cut. You want to get your license, registration and other bills assigned to an out of state address...cut as many ties as possible. Get a mail service in your chosen state. Consider starting a blog which documents your travels showing that you are not living in NY. Ideally, also, try to keep your time spent in NY limited. If you spend all summer in NY, they may treat that as you still living in NY.

This isn't to be alarmist. Lots of people do it and it's perfectly legal...just make sure you are methodical and you shouldn't have to worry about it.