If Mom pays for house remodel and lives here and someday needs a nursing home will the nursing home come after us for the remodel money?

Sicinside, you would need to contact your State Medicaid office to see what are the rules for your State. Medicaid may or may not consider the money your Mom had given to you to remodel the house as a "gift". If they see this as a "gift", then Medicaid would deduct that amount from Mom's care if Mom should go to a nursing home within a certain time frame and needed to use Medicaid, then Mom would need to be self-pay until Medicaid starts.

Now you mentioned "down stairs" into an apartment. How is your Mom doing mobility wise? Usually as we age we will find age related declines. I've noticed that for myself that I just can't use the stairs as safely as I had in the past. My elderly parents were occasionally falling down their stairs in their own home. They were stubborn, refused outside caregivers to come in to help.

If your Mom is ok with using the stairs, make sure your Mom's bedroom has a window that is large enough for a firefighter to break in while wearing their heavy gear, or for your Mom to climb out in an emergency. Also do a radon test to make sure the radon, if any, is at safe levels. Make sure Mom's bathroom is large enough so that if she needs to use a walker later on, that the room can handle the a walker. Don't forget to place grab bars in the bathtub/shower.

Let us know how everything turns out.

Yes, unless she is able to stay with you past the look back period, which varies by state.

Edit- An added complication is dealing with siblings who will see this as preferential treatment, or who will expect you to be her forever caregiver because in their opinion she paid for it.