Make sure to think about batteries before you buy anything. I would suggest looking at the Godox V860III-N TTL Li-ion Flash for Nikon because that lithium pack is super fast for quick shots of the kids. If thats too much, the Godox TT685II-N TTL Flash for Nikon is a solid budget pick, but be careful with AA batteries... they always die right when the baby does something cute. TTL is definitely worth it tho.

Just saw this thread and wanted to jump in! To add to the point above: honestly, once you go TTL, you will never look back. It basically does all the exposure math for you so you can just focus on the kids. I started out being super cautious about non-Nikon gear because I didnt want to damage my expensive D850, but I have had zero issues with these options. I actually compared a few when I was in your shoes. First was the Nikon SB-700 AF Speedlight. It is fantastic because it is built like a tank and the menus are so intuitive. It feels incredibly safe and professional, and it just works every single time. The only downside is it uses AA batteries which can be slow to recycle when you are clicking away at a toddler. Then I tried the Godox V860III-N TTL Flash for Nikon. This thing is amazing!! It has a rechargeable lithium battery which is a total game changer for quick family shots. You do not have to wait for it to charge up between clicks nearly as much as the cheaper ones. It even has a built-in modeling light which helps the camera focus in dark living rooms when the baby is moving around. TL;DR: Get a used Nikon SB-700 AF Speedlight for total reliability and brand matching. Get the Godox V860III-N TTL Flash for Nikon if you want that amazing lithium battery life and faster shooting! Both are way under your budget.

In my experience, the Godox V1-N TTL Round Head Flash for Nikon is the way to go. Ive used it for years and the TTL makes shooting portraits indoors basically foolproof.