There are several relevant papers on coping strategies, but not specific to heart failure.

Search strategy (database and search terms):

Joanna Briggs
Search terms: moral distress

Identified a systematic review that includes some discussion of coping.
How professional nurses working in hospital environments experience moral distress: a systematic review.
Rittenmeyer L, Huffman, D.  How professional nurses working in hospital environments experience moral distress: a systematic review.  The JBI Library of Systematic Reviews. 7(28):1234-1291, 2009.

PubMed

• Search terms: “morals”[mesh] AND (psychology OR stress) AND (adaptation OR coping) AND “nursing staff”[mesh]
  Filters: English

This search identifies over a hundred articles.  You may be especially interested in these references that are available through this search:

Moral distress: levels, coping and preferred interventions in critical care and transitional care nurses.  Wilson MA, Goettemoeller DM, Bevan NA, McCord JM. J Clin Nurs. 2013 May;22(9-10):1455-66. doi: 10.1111/jocn.12128. Epub 2013 Mar 8.
PMID: 23473022

How professional nurses working in hospital environments experience moral distress: a systematic review.  Huffman DM, Rittenmeyer L. Crit Care Nurs Clin North Am. 2012 Mar;24(1):91-100. doi: 10.1016/j.ccell.2012.01.004. Epub 2012 Feb 3. Review.
PMID: 22405714

Innovative solutions: the effect of a workshop on reducing the experience of moral distress in an intensive care unit setting.  Beumer CM. Dimens Crit Care Nurs. 2008 Nov-Dec;27(6):263-7. doi: 10.1097/01.DCC.0000338871.77658.03.
PMID: 18953194

Defining and addressing moral distress: tools for critical care nursing leaders.  Rushton CH. AACN Adv Crit Care. 2006 Apr-Jun;17(2):161-8.
PMID: 16767017

• Search terms for articles specific to heart failure: “moral distress” AND “heart failure”

Identified one article on managing heart failure that discusses moral distress.
Nurs Res. 2014 Sep-Oct;63(5):357-65. doi: 10.1097/NNR.0000000000000049.
Managing heart failure in the long-term care setting: nurses’ experiences in Ontario, Canada.  Strachan PH.