The chick is a week old and you still have them locked inside somewhere. You are well past those first two or three days that the chick can live off of the egg yolk and needs to stay really warm. It looks like your weather is stuck in the mid to upper teens C (or mid 60's F). That's sure sounds nice right now. Some rain is forecast but I can't tell how much or what times of the day. The way I understand it you only have the two hens and the chick, no other chickens. As I read your post you have removed the unhatched eggs. My guess is that you have food and water right at the nest so they don't have to get up.
I leave the pop door open when mine hatch so the hen can take her chicks outside whenever she wishes. Typically that's two or three days after she brings them off the nest. I think part of the reason for that delay with mine getting outside is that the chicks have to manipulate some steps to get in and out of the pop door. But normally by day 3 after she brings them off the nest the chicks are outside. They pretty much stay outside after that during the day. The hen brings them back inside the coop to sleep at night. My outside is a fairly large dirt and grass area, I don't know what your pen looks like or how the ground is covered. I also have a rooster, several other hens, and almost always some immature cockerels and pullets that they interact with. I trust my broody hens and let them decide how they are going to take care of their chicks.
While a hen is incubating the eggs on the nest she seldom gets off the nest. She mostly lives off of stored fat while incubating, that's why she doesn't have to spend that much time eating and drinking and can stay on the nest. Yours have probably used up most of that extra fat so they will look run-down. But that was fat put there for that specific purpose. Now that the hatch is over they need to eat and drink to replace that fat before they start laying eggs again. I'm not sure what's happened the past week after they finished hatching but they should be eating and drinking a lot more, their condition should gradually improve, but that will be mostly fat. Taking care of a chick will slow that recovery some because of all the nervous energy they have. They really should not be that weak right now. It's always a good idea to check a broody hen for mites or lice. Those can weaken a broody hen especially since she is not taking a lot of dust baths and such. If they are infested with mites or lice it is possible they are run down.
I don't know what the area where you have them locked looks like. As far as I'm concerned you have all kinds of options. You can open the door and let the hens decide when to take the chick outside or you can leave them locked inside, hopefully there is some room inside. You need food and water at a level the chick can easily get to it, whether inside or outside. The broody hens should manage either way.
If you wish you can break one of them from being broody. Separating her from the chick for three or four days should do it. Yes, she will be upset for a while, her mothering instinct is strong, but she really will get over it without harm to herself. The sooner one breaks from being broody the sooner she will start laying eggs again. Or you can let them work together raising the chick. It's not the end of the world either way.
I don't know what your plans are for that chick or any future chicks, especially if you get a male. If you are going to hatch chicks you need a plan for that.
With those two that obviously go broody a lot you might want to have a broody buster handy. I use an elevated cage with a wire bottom. Keep a broody hen in there with food and water for three days and nights and she will normally break from being broody. I have three in mine right now, they will be let out tomorrow morning. If that's not long enough for one she will go back in for another three days. That's not being cruel to them. Being broody for long stretches of time can be really hard on them, especially if they don't break themselves from being broody when they use up all their fat reserves. If you give them eggs to hatch every time they go broody you can wind up with a lot of chicks, male and female. In my opinion managing their broodiness is part of responsible chicken ownership, especially with hens that go broody a lot. Sorry if that offends you but if you leave it up to a broody hen she will always elect to hatch and raise chicks.
I wish you good luck. I know how hard it can be your first time and losing that one chick had to hurt. But put some trust in your broody hens, they normally do a great job is given some options.
