Wedding Colors - Will this look tacky

You don't need it any where else. The moms don't have to match. Stick with what you have and don't worry about it. Navy is a neutral and looks good with everything.

Is your FH's uniform navy/dark blue? That would be more than enough to introduce navy into the color pallet if you're concerned about it, but I agree with PPs that the mothers don't have to match. If you want to include more navy because you like the look of it you could consider wrapping the bouquets in navy ribbon and/or giving the groomsmen navy ties and pocket squares.

I think it sounds as though you are going to have a beautiful wedding. Are you going to do programs? If so, maybe add a navy ribbon to the top of those. You can add it in tiny ways like that........ribbons around the flowers.........place cards.

Navy is a neutral so you can have the ring bearer in navy if you want. What color linens are you using? A navy napkin would be a hit of color. Navy vases or other touches of navy in the centerpieces, navy votives or votive holders, so many ways to include navy if you want it.

On the other hand, you can make a decision and leave navy out entirely.

I picked similar colors and the only navy we had was the groom's suit. I didn't let it bother me that navy got inadvertently kicked to the curb; there were bigger things to worry about. The palette ended up being mostly neutrals and pale tones like blush, champagne, ivory, and silver with pops of pale cool-tone greens in the flowers. It was absolutely beautiful. Don't worry! It will turn out well without more navy. BUT if you're deadset on adding more navy, a good way to do this would be to incorporate it in smaller elements (like the ring bearer's suit and more) such as the ribbon on your bouquet, your shoes, the programs and escort cards, table runners, table numbers, chargers, vases, things like that?

Moms dont have to match the decor