Parents approved GC, & outside for last 11 months. Mother fell ill, help

[V1shal]

My parents have approved GreenCard, and they have been outside since the last 11 months; we were planning to invite them so they could get back while the re-entry is valid, but my mother has been hospitalized, and the doctor suggested not to travel for the next three months. This will make her US entry within one year hard. My mother has a neurological problem and could not pursue the route of going to the branch and requesting for reentry permit as that requires talking to an officer and biometric, which she is unable to to.

So, I am wondering:
1. If I could pursue any route while I am US to move their return timeline by 3months(if that is possible)
2. Bring my dad only (not sure if that resets the timeline for my mom as well)
3. Pursue any other route that I am not aware of.

I would be eternally grateful for some direction.

[Dx134]

I'm sorry to hear about your mom's medical difficulties, and I wish her well! That said, I'll just have to be the bearer of bad news...
1. Your presence in the US has nothing to do with your parents' permanent resident status.
2. Likewise, your dad's presence in the US has nothing to do with your mom's permanent resident status. (Maybe immediate family ties can be argued, but I wouldn't bet on that.)
3. If she passes the 1-year mark, your mom might be able to get a returning resident visa (SB-1), as she was legitimately unable to travel due to her medical condition, but it's going to be an arduous process. (Your dad, on the other hand...) The other option for them is to just board a plane bound for the US and take their chances with a CBP officer and most likely an immigration judge. Both of these options are likely orders of magnitude riskier than returning before the 1-year mark.

Reentry permits can only be obtained from inside the US before departing, so that isn't an option. I don't know what you meant by "branch" but if you're talking about US embassies, your mom's medical condition might make her eligible for certain medical accommodations when dealing with them, but I have no idea how that works.

[Mike E]

My parents have approved GreenCard, and they have been outside since the last 11 months; we were planning to invite them so they could get back while the re-entry is valid, but my mother has been hospitalized, and the doctor suggested not to travel for the next three months. This will make her US entry within one year hard. My mother has a neurological problem and could not pursue the route of going to the branch and requesting for reentry permit as that requires talking to an officer and biometric, which she is unable to to.

So, I am wondering:
1. If I could pursue any route while I am US to move their return timeline by 3months(if that is possible)
2. Bring my dad only (not sure if that resets the timeline for my mom as well)
3. Pursue any other route that I am not aware of.

I would be eternally grateful for some direction.

She should come as as soon as she is healthy enough to travel. She should refuse to sign I-407 and take her chances. She will be admitted into the US. The only question is whether she will get an NTA or not. Probably not.