I don't want to get on your case ES, but yeah, Bug is right-- Kiddo seems to have a lot of fuss made over her and is controlling more than she should. It sounds like she's been empowered to do so.
Would your husband be willing to work through a parenting book with you? Something very mainstream and common sense, like Love and Logic or 1,2,3 Magic? I ask this because I think your husband would do better if you approached it as "let's both try this (neutral, non-stakeholder) way" with a very solid and highly regarded book instead of "can you do it my way, please?". If you are BOTH willing to try it someone else's way, there's giving on both sides and common ground in that you are both learning a new way of dealing with these moments which cause such disagreement.
You need to understand that if he is gone and out working most of the day, your husband might like to do some things for your girl. This is one of the harder parts of parenting, ES-- the fact of the matter is that I don't know of ANY couple who parents exactly the same with exactly the same boundaries/rules ALL of the time. You have to be willing to let some things be 'their' thing and know that you are going to maybe be more consistent, more reinforcing of the skills you want her to learn for her social growth... it comes with the territory of being the Stay at Home parent.
What I have learned, fortunately, is that instead of getting p.o.ed at times where there is dissent in how we parent (when my husband and I may not usually be on the same page)-- I have learned to pull my husband aside and ask in a whisper 'hey, can we strategize for a minute?' For example, there are some times when our son is routinely less than cooperative, so making a plan ahead of time, so we both know what our options are. "Hey, since Kiddo sometimes acts up at the restaurant, and you and I both want to sit and enjoy our time, lets make a plan that if he misbehaves, one of us will take him out to the car for a time-out. What do you think of that?" In this example, I am setting the expectation that A. I want to finish our time at the restaurant , B. the 'choice' consequence of 'behave or we are going home' is not going to be proffered, instead, it would be "if you do that again, we'll be taking a car time out" (which gives us more control of the situation) and thus, both adults are on the same page.
Be sure to talk with your husband about these issues--as much as possible-- at calm times and not in your daughter's presence. These are not great 'in the moment' conversations. If you are arguing with him and reacting to his permissiveness in front of your girl, that only makes you look like the meanie. Instead, those conversations might be more effective when he's not stressed. "Hey, I noticed that when she asks for you to do things for her, even when I'm there, you will stop what's going on and do it. Can you tell me about that?" Try to hear his side of WHY he parents the way he does.
Getting on the same page with your spouse as parents doesn't always mean making him accept YOUR proposed page, but writing that book together. It takes practice, and it can be messy, but it's worth it! (and you get to grow as a couple, too!)