L.R.
Is he going to be defensive and angry if you say this to him:
"I think this difference in how we handle these things that seem small to you is this: When your boys were small and were over on weekends, you never really had to discipline them . You tried to keep it fun, but still expected them to remember their manners. Now we have a daughter that needs to be disciplined every day and when she's upset about not getting her way, it's easier for you to make her laugh over something or act silly or distract her, then expect her to listen and cooperate. And then I'm the "bad guy" for expecting her to understand that she's not in charge and she can't just order us around." Add: "When you joke with her about things I have just tried to make an issue of politeness or discipline, I feel bad and I feel as if I am made the 'bad cop.' I know you may feel you did not mean to do that to me but I want you to know what I am feeling so we can work on a common parenting style." (Classic formula: When you say/do X, I feel Y.)
Recognize that? It's almost entirely from your own post.
If you and he cannot have a discussion as frank as that, you and he need to take a parenting class together pronto or see a family counselor for specific parenting help.Certainly try Love and Logic which others recommend, or Supernanny's excellent advice on parenting in her books.
You and dad must get on the same page about how to handle even small things or your daughter will know -- well, she does already -- that she can play daddy off against mommy. And you, yourself, will end up resenting him for making you "bad cop" all the time while he gets to be "fun dad" all the time. I have seen that dynamic with friends and it is very damaging to a marriage. You and he have an issue because as you so rightly note, he has a "fun dad" past with his sons and that is hard to break; it is what seems like normal child-rearing to him but it's not.
Yes, choosing battles is important and you should evaluate whether you're not choosing wisely. But sometimes small things do matter. I agree with you over the toothpaste, for instance. "You get what you get, and you don't get upset" is a good mantra. She does need to learn that she can't wail over her socks or her toothpaste every day and that if she makes a fuss over these little things, you -- AND Dad -- will be less and less likely to say yes to bigger things like doing fun activities. I think that a consequences system, with one chance to fuss; one warning; and a clear knowledge on her part that a second warning brings a specific consequence that is the same EVERY single time -- could really help. She also needs to understand that the issue is not the flavor of her toothpaste; you could not care less about that; the issue is her tone and her repeated "requests" once given an answer. I think you and she need to sit down together when things are calm and good and talk about what you will do, every single time, when she does X. Action X brings consequence Y (losing TV time is often a good consequence if she values that). Treat her as if "you are old enough and smart enough to understand this and I do not want you to feel surprised when I say, 'This is the first warning and you know what happens on the second warning. What will you lose?" "TV time." "Now, will you do Y?"
Do be sure she's getting some choices that give her a feeling of control -- if the sock fuss is because you put out what she should wear, then put her in charge of laying out her own clothes. Or if the TV choice fuss is because your show is on right now, tell her that she can see her show at X o'clock but if she demands or even mentions a channel change again, she will not see it at all. (Or as we might say in our house, "The answer to your request is yes, but it is not yes this instant." It takes a LONG time for kids to absorb that -- learning to wait for what they want -- but it does work; however, Dad simply must be on board too.)