OP, I think it's good for children to see their parents maintaining a normal social life. My parents have very close friends, they really are a proper support network. I have the same. I see a lot of parents vanish into the whole child raising thing and then be amazed to be lacking in supportive friends later in life.
I also think it's good for children and parents not to be glued together all the time, frankly. i used to love our babysitters! In fact I still do, though one has sadly passed on. My parents belonged to a local circle, which was great because they could have date night or social nights, then we moved and two other people did it for pay, but they were so fun.
Just recently mum gave me the ring she wore for dressed up nights out, she has arthritis and doesn't like to wear rings any more.That ring has happy memories for me, I used to sit on the bed and watch her get ready and then she'd tell me all about it the next day.
You don't have to be attached to your kids 24/7 to be a good parent. If you have work, hobbies, social life, you have lots to give them from those things.
As for the saying no.....If you don't learn to say no and if your kids pick that up from you, they're in trouble. Being unable to say no just means being dumped on.