Same-sex couples share many commonalities with heterosexual couples. The day-to-day activities of their lives often are similar, but the social context in which they live differs greatly, largely due to the influences of the dominant heterosexual culture and traditional expectations of gender roles within a relationship.
Conflict doesn’t mean the end of your remarriage, and can actually make it stronger. There are always going to be disagreements; you cannot avoid them entirely. What you can do, however, is become skilled at recovering from disputes by talking about your perspectives afterwards.