While it's tricky to pin down, "Leena" (as in Lena Horne or Lena Dunham) is much more frequently used in the U.S. and Canada, while "Layna" is standard in Europe and Australia. So if you live in North America, you could use the "more common here" argument to break the tie in your favor.
I do think it's a problem. A cultural connotation that links a pair of names is hard to shake, even decades after the fact. "Amos 'n' Andy" went off the air in 1960—likely well before you were born—yet you know about it, and it comes to mind right away when you hear the similar-sounding combo of Amos and Annie. Each name is just fine on its own, but put them together and you have an issue.
In the United States today, Fox would be a bold choice. It would come across as a bit uncommon, as you prefer, but also as appealing to many with its confident sound and origin in a nature word. Short, brisk word names are on the rise, and Fox fits right in with them.
For me, the symbolism of naming our girls after our mothers is more important than loving the name itself, but my husband feels the opposite: Why give your child a name that you don't like, even if it is your mom's name? Do I try to convince him, or do we start over and give up using my mom's name?
–Mom in a Middle-Name Muddle
Your question made me think of President George W. Bush’s twin daughters Jenna and Barbara, each named after a grandmother (they even got the grandmothers' surnames, Welch and Pierce, as middle names). Stylistically, the names are quite different, but as you point out, their symbolism can outweigh the style difference and make them a cohesive set.
But your husband has a point too. He doesn't want to feel locked into a name choice because of the symbolism. I don't believe either of you should try to badger the other into making a choice you don't feel good about.
–Mama Needs Advice
By "two-vowel," do you mean starts and ends with a vowel, like Enzo does? If so, that's a fun challenge for us to take on. Enzo is an Italian name (a shortening of Lorenzo) that has actually topped the charts in France, giving it a strong European vibe.
On the other hand, our two older children have very straightforward, obvious-to-spell names, and I don't want to saddle the baby with a name she'll always have to explain ("it's with two Ns"). I would love to get your opinion!
–One N or Two for Baby Three?
All you need to do is spend a few minutes at Starbucks to know that every single name has the potential to be misspelled, misheard, or mistaken. Laura becomes Lara or Maura or Lori before you can say "grande half-caf skinny mocha." But everyone gets their coffee and life goes on.
–Stuck in the Middle
You ask how to handle your mother's disapproval of your wife's preferred name. I can reassure you that your mother is far from the only grandparent I've encountered in this column to complain about the name of her grandchild. The vast majority of them (eventually) learn to keep their complaints to themselves.
I'm afraid you are an outlier on this. The majority doesn't share your instinct: The spelling Harlee is overwhelmingly female. There were 300 baby girl Harlees in 2014, for example, and just 10 boys. In the same year, 407 boys were called Harley (along with 940 girls).
Loving the sound of a name, but not its meaning, is a tough spot to be in. After all, name meanings are tricky to pin down and can be misunderstood. And the sound is what you hear every day when you speak your child's name. Thousands of parents every year choose names based on sound, without giving meaning much thought—otherwise, would anyone choose a name that's said to mean "crippled" (Claudia) or "unlucky" (Mallory)?
–Friend in Need
Not really—for starters, Maggie is already a nickname—but the good news is that you're well positioned to give your friend a nickname yourself. This is just what friends are for! Does she need a nickname because she doesn’t care for Maggie? Or just for fun, as a symbol of your close relationship? Let's look at each possibility in turn.