You're probably going to have to have a chat with your mum about this because if there's not a good specific reason for her concern, then it would be helpful to you if she could relax on this issue because it's impinging on your ability to enjoy your life as an adult. She should care about that and if she doesn't that tells you something. Ideally you could avoid the whole issue by meeting your date somewhere other than your house, although it will be awkward if you are unable to return home with them at any stage. Can your sister or any of your friends give you a ride to meet your date elsewhere?

A point of confusion I have from your post is whether you're asking about your rights to date people, or just your rights to have them pick you up from the house. As far as dating people is concerned, you say you're 25, you can do what you want neither your Mum nor your sister have any choice about it. You do not have to justify this or use your recent birthday as an excuse for anything because there's nothing to excuse. Whether you want to date people is up to you and you alone.

If your Mum specifically requested that you not bring your date to the house it would be rude to just ignore her, particularly if she has some special reason to be extra careful, but it's also a very strange request for her to make of her 25 year old adult-child so you'll definitely need her to give a pretty good explanation why you shouldn't do this. Similarly, it's a very strange situation to be in that you're worried about your sister watching camera footage of you as some kind of evidence of wrong doing, why is she in a position to do that and why would she want to? How old is she? Such behaviour is bizarre and controlling.

A lot of the details of your post sound like you've been living in strange and possibly abusive circumstances where your mother and sister are putting a lot of effort in to monitoring and controlling you, which they do not any rights to do. In most places I know of, a person is legally an "adult" at 18 years of age, how long have they been doing this to you? Were you allowed friends and relationship in school? What about afterwards at work or university?

Do you want to continue living with your mother? It might be a good idea to start gaining some more independence in your life so you can safely choose to live in a different arrangement if you want to. No offence, but the way you write does sound strangely young and naive for a 25 year old, especially the idea that you need to have either your mother or your sister around to look after you. Do you have friends that know about your living arrangements? Do you know many people outside of your house? If you tried to make friends and spend time with them, is that something your mother would try to stop you doing? It sounds like you're very isolated and your Mum is keeping it that way on purpose. Unless there's some very specific context that can explain all these details, then it sounds like there's something very wrong about how your family is treating you.