The first thing you can do is look at the power of attorney documents to see if they contain a system for resolving disputes. The best option is to try and come to an agreement on your own. If that doesn’t work, you can try mediation. For more information about mediation, go here: http://www.elderlawanswers.com/family-strife-over-elder-care--consider-an-elder-mediator-14857. Unfortunately, if the agents under the two powers of attorney still do not agree, the only solution may be to petition the probate court to resolve the dispute. The court will decide what is in the best interest of the parent. Going to court costs time and money and should be used as a last resort.
For information on how to avoid a conflict between your POA and health care proxy, go here: http://www.elderlawanswers.com/avoid-disagreements-between-your-power-of-attorney-holder-and-health-care-proxy-8704.