Almost all my clients have the same issue as yours.
So your challenges are not unique.

While making positive business progress is a wonderful thing, external growth must come with relevant similar pace of internal growth.

It seems that you are using the same old management approach/ style despite your business has grown from 1 or 2 people into current size. It is no more purely a number game now, mismanaging people will lead to loss of knowledge, valuable customer, profits, and growth potential.

Your backyard is having fire currently means your internal support team is having some challenges and you may have uneven growth in some business functions - immediately you should investigate the following areas:
1. Review your management approach/ style and system
2. Review whether you are capable to manage C-level employees.
3. Review your human capital policies and culture diversity
4. Review, whether you have clear/ appropriate a) accountabilities, b) roles and responsibilities, c) committed budget, d) monitoring and control system, e) KPIs, etc
5. Revisit your mission/ vision/ expectations, adjust if necessary.
6. Review workflows and communication models to identify what has triggered the conflict(s).

I think the above should help. Upon making the reviewing, you may already have action plans. If you still have problems, feel free to drop me a message

Tell your COO they are causing problems with the older employees by not respecting their space AND not sticking to the agreed upon process for handling the situation. Remind her that if someone were to not follow an agreed upon process under her direction, she'd likely be extremely upset.

Tell her it's her problem to solve and you expect it sorted out immediately.

Done

As owner, best you jump in + resolve this.

Get all parties together + talk about problems.

Setup a policy to resolve future similar problems.

Note: Growing pains are expected, as revenues grow.

If new COO is bringing more value than old employees, then prioritize her approach.

If not, the prefer veteran employee's approach.

The single toughest part of being a CEO is dealing with this type of evolution.

I'm happy to have a call with you.

Likely many others can provide a call too.

And ultimately, your job is managing revenues... rather than being friends with anyone.

I know this may sound rough + you're at the wheel + must steer the ship in the best way you imagine.

You are the ultimate, final say in all matters.

You have got some solid advice here. I would not be your guy to jump on the call, however will chime in with a couple extra things to keep in mind.

Only 2 points I would add.
1. It is you 4 VS growing the company. Not VS each other.
2. None of them are wrong, it is just different ways (balancing the way it was vs growth)

Good luck, handle it fast or lots of time and resources will be wasted.

I work with a number of clients to improve their leadership skills and I see this more than you would think. There are a couple of ways to look at it.
More often than not, you see fallout of the veteran employees and one or both could possibly leave you. This is ok. You have prepared for this and have the systems and processes in place to cover the gap until you fill the positions and train the replacements in the shortest time possible.
The second scenario is that you are able to get all three of them in a room together to has it out. You will need to facilitate this. It will take a good deal of planning and framing to understand that no one is to blame or wrong. It is time to get your team on the same page, letting the veteran employees understand that she has been brought in to execute your strategy for the company, not a hidden agenda. I would also suggest some leadership coaching to address change management.
I'd love the opportunity to chat to you more about this and see how I can help. Feel free to set up a call with me.

An important guideline when coming into a leadership position with senior staff is to take 2 years before you make major changes. The first year you mostly go with the flow and try to fix blatant deficiencies. By the second year you have built trust and a relationship and know the company intimately. Changes can be consistent and more bold by year 2. After year two you can start weeding out those unwilling to adapt to the culture and trend you are creating. If she is going in and making waves I would encourage her to back off and focus on building relationships. Those employees probably know the company better than her and she could use their experience.

Look the problem I find in the question is discourse is dominated by normative ideals that esteem the positive attributes of leaders but there is also the failure to acknowledge the dark side of leadership and its influence can distort efforts to learn more about the leadership process. Leadership rests in the eyes of the beholder. It is bestowed upon the leader by followers; thus, I believe that the new COO must look through the eyes of the veteran to solve the issue.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath