The following is exaggerated to make my points clear, but not intended to imply anything about you, op, or your family. I've written principally, but used your info as data for the arguments I'm making. I also understand that you are struggling and you and your dp are not at this point very clear about how you want to communicate as a family about conflicts that arise between your members, so this is not meant to indict you at all; it's just the most accurate way I could think of at the moment to express it.
What I don't understand is the unnamed alternative when gentle discipline isn't "working." What are you going to do? Anything you choose to do to or with your children is going to require at least as much consideration, analysis and understanding from your children in order to "work", but the less opportunity you afford your children to work through your life together, gently, the longer you will have the same issues. So, for example, you could punish your child instead of explaining why it's not okay to act obnoxiously in company, but this still requires that the child recognise specifically the behaviour that you deem obnoxious (by what means? Are you really not going to explain it to him?), then reason that if he does it, you will hit him/put him in his room/take away things he values/etc....
You are no further ahead by not engaging your children: the same processes and mechanisms are required for them to determine whether or not they are behaving in a beneficial way, what you approve, and what the consequences are. Without gd, though, you just make their options and, consequently, their world, a little or a lot smaller.
My favourite question to people who punish is: "Does it work?" Inevitably, they say, "Yes, of course." My reply: "So you only had to do it the once, then."
The point is that punishment is a false economy (except in specific circumstances and only pertaining to adults, not children). What you punish, you have neglected to adequately or clearly identify as a problem and then to add insult to injury, you also neglect to solve the problem. So the children behaved in a way you didn't enjoy. Then they are forced to stay in their room all day, apart from you, feeling rotten and unloved. Problem solved? Hardly. You could do this until they're grown, but it still wouldn't ever become the solution to a problem. But the worst part of this is that no problem has been clearly, rationally defined. "I don't like how you behaved today" is not even close to adequate for the conclusion of a discussion, let alone instruction in what to do and not to do, which doesn't even address the underlying issues related to reasonable expectations according to realistic standards for either the children, or you and your dp.
You are no further ahead by quitting gentle discipline, which just means a willingness to act compassionately while guiding one's children to adulthood. I cannot see how that wouldn't "work", unless there is a faulty underlying premise such as defining "work" as that which gives me veto power and fear-evoked appearance of respect. I am assuming you would prefer the former, which is why you have been gently disciplining to begin with.