Late to the party, but if you want sharpness across the board without breaking the bank, you really need to look at the Nikon AF-S DX NIKKOR 18-140mm f/3.5-5.6G ED VR. It is a massive step up from your kit lens! The optical construction features 17 elements in 12 groups, including one ED glass element and one aspherical element, which keeps aberrations super low. You get that extra reach for family events while keeping the wide end functional for landscapes. Honestly, for around 300 bucks used, it is fantastic value. It uses a silent wave motor for fast, quiet autofocusing, which is perfect if you are filming random clips of the kids too. It is basically the Swiss Army knife of DX lenses and worth every penny.

Just saw this thread. Honestly, dont overthink the numbers. For that budget, you have two solid choices that are way better than the kit glass.

• Nikon AF-S DX NIKKOR 35mm f/1.8G
• Amazing for family shots indoors, super sharp, but you have to zoom with your feet.
• Tamron 18-200mm f/3.5-6.3 Di II VC
• The ultimate travel convenience lens for the price. It covers everything from landscapes to telephoto zoom without swapping.

Honestly, ditching that kit lens is the best move you could make for your photography! If you want a one-and-done travel companion that handles family shots like a champ, grab the Sigma 18-300mm f/3.5-6.3 DC Macro OS HSM. I took this exact beast on a three-week trip through Europe last year and didnt have to swap lenses once. The zoom range is insane, covering everything from wide-angle landscapes to tight portraits. It uses an optical stabilizer that is just amazing for handheld shots when the light drops. The sharpness across the frame is fantastic for a superzoom, and you get that sweet macro capability for close-ups of flowers or whatever. Its basically the ultimate Swiss Army knife for your Nikon. You will absolutely love the versatility!

^ This. Also, reliability is everything when you are traveling, and unfortunately some of those third party superzooms just fall apart mechanically after a couple seasons of heavy use. I had issues with mount play developing way too fast on cheaper glass. If you want something built to last on a D3500 without breaking your 300 dollar budget, look for a used Nikon AF-S DX NIKKOR 18-300mm f/3.5-5.6G ED VR. Nikon's newer version is definitely a bit pricier new, but clean copies pop up used all the time. The weather sealing and build quality are just in a different league compared to the kit plastic, and it wont let you down mid-trip.