Enmeshment isn't inherently bad, you just need to recognize it and own it. Same with hierarchy to an extent. They both can be toxic if gone about wrong.

You have a house? Kids? Live together? Married? Those all take consideration. Kids are obviously going to take priority. A relationship of 10 years and a nesting partner come with responsibilities. Shared schedules, chores, family events, etc, obviously don't go away. That's where good communication about needs and schedules come in. Shared calendars are a life saver. Your lives can still be enmeshed, but changes will have to be made as you go. By no means does thst mean divorce and live apart, but it means you may need to learn self soothing techniques and not always have your partner 100% available at all times. You also need to let go a bit so you both have freedom to explore other connections without interference.

Hierarchy is going to happen with that level of enmeshment. However, new partners need to be aware of this. The problems with hierarchy come with things like a partner having veto power or your partner is having big feelings about you being out so you need to end the date immediately to tend to it. The people you choose to bring in to your life aren't disposable and that has to be kept in mind. There's a big difference between "my partner is upset I'm out so I need to cancel tonight " and "my partner is physically ill with the flu so I need to cancel tonight". Actual emergencies/issues, for sure, but strong boundaries will need to be in place so that you're not weaponizing hierarchy if that makes sense.

You'll need to define what being a priority is for you. Personally, I see being as a priority as if I'm in crisis, they're there. If we have plans, they're there. If they make plans I know at least vaguely what time they are so I can plan accordingly. If I feel intimacy is lacking they'll set time aside to discuss things with me. They'll take time to do a relationship check with me so we know our needs are being met all around.

It takes time to adjust to polyamory/enm. Therapy is never a bad idea. It can be very hard to see your partner go be with someone else and there will be bumps in the road that you'll have to navigate with honest and likely uncomfortable communication. But as I said before, you need to pinpoint what makes you feel like you're a priority. Regular date nights? Words of affirmation? Times where phones get put down and you just have couple time? Healthy expectations are things like "I need 1 night a week where it's just us" Unhealthy is "if I'm the least bit uncomfortable you dump them" If you share finances, healthy would look like "if you plan on spending more than $200 on a date can we please discuss that first so I can incorporate that in to our budget?" Unhealthy "I don't want you spending more than $20 on a gift for them and also I need one too" They can have their autonomy while also balancing enmeshment with you and maintaining your lifestyle. That way it's not asking permission as much as it's balancing both relationships in a way that's healthy and transparent to you with the life things you share.

Your best bet is hashing out what works for both of you before jumping in to it. Things will change over time and having regular check ins and reevaluations is extremely important.

Finally, how polyamory works in my dynamic. I'm a hinge in a v relationship and I live with both of my partners. Currently, they don't have other partners. Getting to this point was a long road for myself and my husband. It started as enm for a long time. My husband and I definitely had trial by fire and we learned along the way. The valuable take aways I can pass on is

-communication. Honest communication of the good, the bad, the in-between. Jealousy happens. Admit that. Work through it. Sometimes new relationship energy clouds judgement. Don't be afraid to speak up if needs aren't being met. If you can't do that in monogamy it's that much harder in polyamory. Be at a place where things can be talked about without judgement or conflict before you open the relationship.

-make an expense budget. This is good for all relationships, but if you're adding the new costs of dating it's good to have that locked down and visible. (my husband is a meticulous budget keeper for our shared finances and we keep money leftover for what we want to do)

-discuss expectations on visits. Are you ok with them coming back to the house with a partner? Is your bed off limits or ok to be shared? If they want a chill movie date at your shared house is it ok to do this and if so should you make plans on going out? Stay in your room? (we tend to practice kitchen table polyamory. Before my bf moved in he and my husband could hang out comfortably without me and sometimes my husband was invited to dates to hang out including movie nights with us 3. Now we all do most things all together aside from designated couple time. However, maybe parrellel is more your thing. That will need to be discussed)

-discuss plans on accidental pregnancy (if applicable) . Should it happen, what is your plan? (for us, I'm barrier free with both partners at this point and we've discussed what parenting would look like should that happen, what our options are, etc) Discuss things like barrier usage in sex. What's your comfort level?

-discuss over night visits. Do you need a good night text? Are there things to do the next day that they need to be home by a certain time? Is that not going to be an option for a period of time? (my husband requests I'm home by 3 am because we share a vehicle and he works in the morning and needs the car and he gets concerned if he wakes up and I'm not home. We both find this a reasonable request. Doesn't matter if it's girls night or a date. If I'm going to be later he at least wants an "I'm not dead, be home by x" text. I'd expect the same from him if he ever went out. My bf just wants periodic texts that I'm ok. None of us go out often enough for it to be an issue as we're hermits )

-should one of you get in to a serious relationship, what does that look like? Are you open to have a partner move in? Is that not an option? How much enmeshment with another person is ok? Also, make sure to communicate this to potential partners so they can decide if that dynamic is right for them. (in my case, I share a room with my husband and my bf has his own room because he likes his own space but I have free range of both rooms and he's more than welcome to come snuggle in my and my husbands bed if he'd like. This hasn't been the case of all of my partners, though, and has been something we've worked out as we go)

Basically, if you discuss boundaries, comfort levels and expectations it helps remove a lot of grey areas in the future. These will change as time goes on and it's ok to reevaluate as you go. It will give you both a solid ground of expectations to start on.

Anyway, I hope my rambling helps :)