Can I switch from active to NG or Reserves while in my first contract?

PVT (Join to see) look for installations close to your mother and request a compassionate reassignment via 4187. Work with your local command. https://www.hrc.army.mil/content/Enlisted%20Compassionate%20Actions

If your mother can't live on her own, consider making her a dependent so she can live with you. https://www.dfas.mil/militarymembers/SecondaryDependency/secondarydependency_Army.html

Your profile has no info available in it so I can't see where you are, your MOS, and what you are doing. I'm assuming you're still in IET. You can't do anything from there, ideally you want to catch this before you have orders. You need to talk to your chain of command. You can't sneak around and hope to work a drug deal,

Yeah sorry man, you have to finish out your contract first.

Not on your first contract. At best you can get an early release 180 days out from your ETS to contract to another component, if approved.
Your particular case sounds more like you need an entry level discharge.
You would want to get that due to hardship, (your mother's condition) before they process one on your behalf for Depression.

If you get that, you can think about joining the Guard later, after you are back on your feet.

One you've signed your contract and have shipped, you're locked into AD until you've finished out your contract, you should have thought about this beforehand.

No. On the first contract you are stuck. You cannot go from AD to NG, RE or IRR. You can upgrade on the first contract but not downgrade. However there are avenues open to you. Go to your base Chaplain and talk to him or her. They will be able to help in ways you might not expect or think of. Also see about a compassionate reassignment or see about making her your dependant.

I get that it sucks and that you feel like there is nothing you can do about it, but you have to keep your head on your shoulders and emotionally straight. Finish out your AIT and graduate. The complete your first contract.

If anything hasn't changed, you can either go NG, Reserves or IRR after your first contract. For instance on an 8 yr contract, if you sign up for 3 active you can do the rest in any of the other 3. Just do what you need to do to make it a smooth transition. Good luck

Call the Red Cross for assistance!

LTC Jason Mackay has provided you the best course of action.

Just a suggestion; while on active duty, do not make the same mistake that many young soldiers do, because “they don’t get their way.” Be the best soldier you can be while in training, then onto your first assignment...it’ll make time go by fast. If you do the opposite, and complain, fail PT tests, Weapons qualifications, etc, you’ll develop a reputation of being “one ate-up soldier” and things will be more difficult for you, when you’re putting in your request and as your paperwork travels thru the “slow” system...your reputation will follow you. I do agree with LTC Mackay, regarding a Compassionate Reassignment. It’ll be an active duty assignment closer to where you want to be. Before your contract is over, you’ll probably see a Reenlistment NCO. That’s when you search, with the Reenlistment NCO for a Reserve Unit or National Guard Unit closer to your home; be willing to change your MOS though. Once they find a slot and MOS for you, you’ll reenlist into it. That’s kind of the “nuts & bolts” of it...unless things have drastically changed since leaving 8 ½ years ago.

It's been a long time since I was in but that was always no for many reasons.