Is it legal for me to obtain a power of attorney for ailing brother if someone has mine?

A power of attorney just indicates that you've authorized someone to act on your behalf for certain purposes. Yes, your question is "legal." It might simply get problematic if you have multiple people in the chain have problems at once. (It's not like the person you give power of attorney can start waving around the power of attorney your brother gave you and take over his.) If you're having some problem where you need to grant someone a power of attorney, you perhaps shouldn't have one over your brother, or your brother should specify an alternate. Do also keep in mind if your brother is "ailing," that a power of attorney normally stops at death or incapacity.

If you're both having some problems, you should probably be consulting a local attorney about the situation to ensure you set things up correctly, such as via advance health care directives, durable powers of attorney, trusts, wills, whatever.

Yes it's legal. But you should change the power that you gave to someone else to exclude the power to deal with your ailing brother's property, unless you want to authorise that person to exercise the PoA in respect of your brother, in which case:

1. your brother's PoA to you should authorise that, and

2. you should still change your own to make it clear.

The main thing is that, whatever you ultimately decide, it needs to be clear to someone on the receiving end of the authority, someone who is going to be reading the powers of attorney, that the original principal has in fact authorised that particular agent to do or sign whatever it is he's trying to do or sign.

That becomes a bit confusing - if you're disabled for some reason, the person with PoA over you now is in charge of two people, basically. Better to give power of attorney to someone who isn't likely to need their own care right away.