I kind of understand how your wife feels about the word "lover" but for me it sounds a bit hokey, as well. We, after a year and a half, haven't settled on regular "names" for what we are. Before we even embarked on our quad relationship, though, we were already referring to each other as "other husband/wife", because on the weekends, Easy and Asha would work at the Renaissance Festival, and Sunday and I would usually end up watching the kids together, wandering around the Renaissance Festival as a conglomerate family. People who didn't know us well often assumed that, indeed, Sunday and I were married and all four kiddos were ours. That's why I call him Sunday--he's my Sunday husband. The kids used to call him their Sunday daddy. Lately, Monkey's taken to referring to them as her stepparents, which is something I'm not sure if I like. It just sounds like something that makes them less, to me.
Asha most frequently refers to herself as Easy's other wife or second wife. She hardly ever uses the word girlfriend in that context. However, she has referred to herself as my girlfriend. She has said that she likes the word lover and enjoys being called that. Easy has used it once or twice, but I think he's kind of clueless as to what to call her.
I haven't got any idea if Sunday ever calls me anything, though once we did discuss what we should call each other and he mentioned calling me his Sunday wife.
I like the person who refers to their sweetheart as "koibito", which is Japanese for sweetheart or romantic love. If I could get comfortable using that, I would totally do it.
PS--Easy and I were handfast before we were married. It's in effect a trial marriage, and the original (so we were told) handfasting was for a year and a day. If there was a pregnancy, the marriage became permanent; if there was no pregnancy, the couple could decide whether to stay together or go their separate ways. Because of the laws in the state where we live, when we had our handfasting ceremony we basically had a common law marriage.