Would you let your teen do these for an Anime Convention?

Looks like you need help from a convention veteran. :3 Let's see what I can do here.

What convention is this? Sometimes the larger conventions cost more money to get into or work towards. Save up the money you need, and trust me, you'll need it. If you pay at the door with that much money, bring at least twice that so you can spend the rest. As you've got a while until then, you can work by selling things on eBay around your house that you don't need, or if you're talented, open a shop on Etsy and sell things you've made. That's the easiest way for a teenager to make money, usually guarenteed, as the internet can't fire you. If you know for a fact you can go at least two days, it's easiest just to buy a weekend pass, as that usually saves money on the cost of two days instead of paying for both at the door.

With the actual cosplay, if you want to make a good impression on your grandad, try to make your cosplay yourself, if you've got the decent sewing abilities, of course. If not, you'd be amazed what a trip to Goodwill or a second-hand shop and a sewing machine could do. If you've got making/ordering it taken care of, I would go for a more modest cosplay to keep your grandad happy. Momo would be the better choice of the two cosplays you were considering, as Yoruichi's outfit is decently tighter and might come off as a bit more strange to your grandad. Momo's isn't very tight, relatively loose, and you'd still look very cute as a Momo, so it's more or less a matter of what appeal you're going for: sexy or cute.

You are going to want to probably order the ticket early, trust me. The prices skyrocket by convention week. Try convincing them about the benefits and explain to them how much the price is going to change by the time you need to pay. It's well worth it in the long run to order online.

As far as staying in a hotel room goes, I'm also 14 and I've never been able to stay in a hotel room alone for conventions. I've only been to one convention where I stayed in a hotel room, and that was with my family, for my birthday, all three days of the convention decently far from where we lived. The other two conventions I've been to, which was the same convention two years in a row, was in the same place both times, and I would just drive there for one day and come back (there wasn't an excruciating amount of things to do there that I wanted to come back all three days, let alone get a ride to do so). Definitely call up some friends that you know could commit to this, help them organize and plan for it as well, even make their cosplay if you need to, as the world is a dangerous place and it's justified about her concerns for letting you stay in a hotel room.

If you run out of time to do the cosplay, you'd be amazed what just one trip to a thrift shop could do for you, and you could try to get rush delivery on a wig if the cosplay calls for one.

If everything else fails, ask to go to this convention as an early birthday present, or a late one, if it'll have already passed by then. Ask for everything you think you might want for Christmas, and then ask for this, maybe only this, for your birthday.

All in all, I wish you the best of luck, and I'm still curious what convention this is, as I'm planning to go to one in December and one in May, and possibly one in July. Have fun!