How big is the living room exactly? If its small, even the 50mm might be a bit tight indoors on a crop body. A decent option for your budget is the Sigma 30mm f/1.4 DC HSM Art. It works well for wider portraits and has that fast aperture youre looking for. The bokeh wont be as compressed as the 85mm, but it's way more versatile for family stuff...

Honestly, if youre worried about space, definitely skip the 85mm for now. I tried using one at a family dinner once on my crop body. Backed into a corner trying to fit everyone in, it was a total mess. On your 90D, that 85mm behaves like a 136mm lens... thats way too much zoom for a standard living room. Youd be lucky to get more than a close-up of an earlobe if you're standing across the table. The Canon EF 50mm f/1.8 STM is the safe, reliable choice here. Its basically the gold standard for a reason. Its cheap, sharp, and wont fail you when the lighting gets a bit moody during the cake cutting.

• indoor use: you actually have room to breathe and move around without hitting furniture
• backyard: still gives you that nice blurry background everyone loves for portraits
• weight: its super light so you wont get tired chasing a kid around for two hours
• value: leaves you plenty of money left over from that $450 budget for a nice strap or bag If you really want to spend the whole budget, maybe check out the Sigma 30mm f/1.4 DC HSM Art for Canon. Its great for indoors because its wider, but the 50mm is such a solid starting point. The Canon EF 85mm f/1.8 USM is gorgeous outdoors, but for a birthday party where you're bouncing between the living room and the grass, itll just frustrate you. Stick to the nifty fifty, it's a classic for a reason.

Like someone mentioned, that 85mm is just gonna be way too tight for a house. I tried using a long prime for my nephews birthday and unfortunately it was a total letdown. I spent the whole time backing into furniture and still couldnt get the shots I wanted. It was really frustrating when the gear I thought was gonna be great just didnt work in a small space. I'm curious though, are you planning on just taking close-up photos of her face, or do you need to get her whole outfit and the background in there too? Also, is that $450 budget just for the lens or are you hoping to get a filter and some extra batteries with it? Just wanna make sure you arent disappointed with the final cost.

Honestly, I have gone through so many lenses on crop bodies over the years and the space issue is real. I used to think the 85mm was the holy grail until I tried shooting a kids party in a tiny kitchen... lesson learned the hard way. If you want something that is actually gonna work without you having to stand in the hallway to get a shot, you gotta look at the 35mm or 50mm range.

• Canon EF 50mm f/1.8 STM: Super reliable and sharp for the price. Its great for those headshots in the backyard, but like others said, it gets cramped fast inside. Its my go-to recommendation for beginners tho because you just cant beat the value.
• Canon EF 35mm f/2 IS USM: This one stays on my camera way more lately. In my experience, the image stabilization makes it way more reliable for low light indoors than the 50mm, plus the focal length is much more natural on a 90D for environmental portraits. Might have to hunt for a used deal to hit that $450 mark but its worth it. I really think the 35mm is the sweet spot for what you are doing. Its just way less stressful than trying to make a long lens work in a small house. Let me know if you need more help narrowing it down!