Don't stop your daughter using the bike. That's punishing her for her relatives' behaviour and will make her resent you and not them. Perhaps you could make it more appealing, with ribbons on the handlebars and a basket or something? Or buy her a nice helmet?
With regards to the parents, you need to talk to your DH and ask him what he wants to do. It sounds like he doesn't like them very much, could you all go low contact? So perhaps your DH goes once a month on a Saturday, or whenever works, and then maybe every other month he takes the children, if you think the family might complain about seeing them.
I know most people will say that your DH needs to stand up to his family, and they are right, but it sounds like he doesn't have the confidence to do this at the moment. My DH is the same. He is scared of his parents, although he doesn't even know that he is. He is desperate for their approval, for them to tell him well done. They never will, and he is slowly learning this. So in the meantime, I stick up for him whenever I can. He shouldn't let them speak to you or the children badly, but if you don't like the way they are speaking to you, the children OR your DH, call them out on it. Demand that they explain why they're laughing, or ask them to explain their comments, if you think it's rude. Why do they think it's ok for them to talk to you/DH/DC like that? Call them out on it every time, and they will either stop it, or they'll go low contact themselves because they won't want the arguments.
I used to get into such a state over my in laws, but now I just call them out on it - I don't care whether people think I have a DH problem, I know that he really struggles with where he belongs in his family of origin, and doesn't know how to deal with them. I don't lose anything if they cut me out, so I can tell them not to speak to him in the way they do.
I also hold the power - if they piss me off, they don't see my children. So things have got a lot better. Still not brilliant, but better than they were.
Don't take any shit from them, stand up for your children and your DH, encourage him to stand up for himself and for you, and try and see them as little as possible.
And don't take the bike away from your daughter. It's not her fault.