How does lodging/travel work when I'm over 200 miles away from my Reserve unit?

PFC (Join to see), the USAR has a policy for Lodging In Kind (LIK) for Soldiers like you and myself that have to travel 50+ miles for Reserve duty. Below is the link for the DoD policy. If there is a newer policy, I can't find it. That being said, please reach out to me via email here or [login to see] or even call me directly on my personal cell @ [login to see] . Because what you have been told is...quite frankly....a massive crock of shit.

https://www.esd.whs.mil/Portals/54/Documents/DD/issuances/dodi/122509p.pdf

Whoever is telling you this is illegal is a barracks lawyer, i.e. someone who does not read regs.
Like many things, Home Station Lodging is authorized. Authorized does not mean funded. The Army Reserves and Army Guard stopped receiving funding for this before the war started. Until about 5 years ago the Guard and Reserves were able to divert GWOT funding for this, but that went away, too. This is handled at BDE level with a Unit Travel Card (UTC). Since we are no longer funded, units are required to provide cots on the drill floor for those traveling over 50 miles. If they are not doing that, then they are wrong and that needs to be brought up to the chain of command.
You cannot just "skip" drill if you can't afford it, that is called AWOL, and 3 AWOL drills in a 12 month period will get you a reduction in grade and a discharge that doesn't qualify for benefits. If you cannot afford to go to drill, you need to request an Authorized Absence or request to SUTA with a closer unit to you (Reserve or Guard).
Also, you need to find a unit closer to home (Reserve or Guard) and transfer to that.
You can transfer now and take up to two years to get the reclass done down the road.
This would be easier if we knew what unit you are talking about, your profile still lists your AIT as unit of assignment,

I’m not familiar with how Reserve works but a 250+ miles commute for a weekend drill is insane. You need to transfer to a closer unit. Yes, most likely you’ll have to reclassify but I’ll assume that most of the Reserve MOS schools are done during summer; and that is something you should be able to work out with the gaining unit. You could do some research and explore what type of units are closer and potential MOS schools thru ATTRS to have an idea. Again, that’s a long commute and potentially dangerous. Take care of yourself since apparently your Reserve CoC ain’t doing it!

Your unit is required to provide lodging if you live outside the commuting distance. Someone in your chain of command is dropping the ball, because 250 miles is clearly outside the commuting distance. I don't know how far up your chain of command you have gone, but clearly there are some things wrong here.
For starters, there is no way that I, as a male NCO, would have suggested that a female E-3 stay at my house with me. There are way too many things wrong with that. Also, your command should be concerned about your well-being, so that you can perform your duties adequately. Asking you to commute 250 miles without authorizing lodging or providing quarters shows no concern for either. It would appear that they are more concerned about the unit's budget.
If you haven't talked to your First Sergeant, you need to. I also suggest that you contact your unit's finance section. They will be able to tell you what you are authorized for lodging expenses. Unless something has changed in the last three years, you are not entitled to gas or mileage reimbursement for drill. You are entitled to reimbursement for lodging (within limits) if government quarters cannot be provided. If all else fails, there is the Inspector General (IG), but that should be your last resort.
I did make the assumption that you are female based on the spelling of your name, if I'm wrong, I sincerely apologize.

PFC (Join to see) - Your unit is required to provide Lodging in Kind (LIK) to any Soldier who travels more than 50 miles to their reserve duty. I would also look at requesting to be assigned to another unit.

Anything over 50 miles and you are eligible for Lodging. This is something your UA should be handling for you. Now, I am not sure how travel pay works for the reserves side but, if my memory serves me correctly at 250 miles you should be eligible for 2-3 days lodging.

I’d get with your UA and like it’s been said send it up your chain of command and someone should take care of you.

Side note, maybe further along in your career you may want to transfer units to something closer to home.

Not Sure How It works Now... But They Used To Have To Provide Some Form Of Housing If You Were A Set distance Or Find A Reserve Unit Closer To Your Home There Should Be Some Guide Lines It Your HQ...

Do they not have any cots for you to sleep on in your drill hall at night. Thats what my guard unit does during drill (when not sleeping in the woods lol)

For Guard and Reservists there is no form of forma lodging system. Depending on the unit, you may get to sleep in the Drill hall. Start the process for finding a closer unit is the best answer I can give you. If you go that route, you need to do the work, don't expect others to do it for you.

Someone in your unit should have access and make arrangements with a local hotel for those needing Lodging in kind. Not sure why your unit is not participating unless they think it is too much of a hassle.