First of all. Good work. That situation is a challenge.

I am writing this answer, more to myself than to you. Things and methodology that I need to put into practice more often. So I do not know what is the "best practice".

I first start with a single ambient exposure without flashes

I. I hope you mean "bracketed multiple exposures". Remember that the very first option you have is to make some HDRI techniques, or even some dodge and burn over different exposed layers.

II. One thing that would be useful to analyze your specific case is where the flashes are and where you are aiming them to.

I have some clues tho. (A) My diagram does not mean that you are using a snoot. It is only showing where I think the light is and I am circling the zone where I see the shadows.

But in an interior scene, we have large areas of light bouncing light to the opposite side. (B) so my first option would be simulating what would a light on the spot (C) would bounce light? The answer is on the ceiling.

III. In general, I would bounce the light to illuminate the opposite side. First on the ceiling and the floor on a different shot. Thankfully the ceiling is white!

The flor you have the additional problem that is a glossy surface. Probably you can carry a big white fabric (I would carry several m. of it). Try not to use a synthetic fiber, because they cast some magenta-purple color. You can even use it to cover color furniture so it does not cast a lot of colored light.

These zones are a good excuse to use them as light sources. I would fire flashes on the second floor.

IV. I do not mind a different color on the light entering the window and the light bouncing on the interior it is expected, but you could get some LEE filters. Specifically, get some CT (orange) and CTB (blue, just in case). It is way cheaper if you buy one sheet of gel, that way you can cut several pieces and have spare gels in case they wear out. By buying one or two specific colors you will know how they respond and you can get a new gel with the same color each time.

In case the full CT is too strong, as the light is bounced, you can cover just a fraction of the flash head and you will get a fraction of the color cast. Sometimes I use the flipping plastic pice some strobes have to spread the light when you need to use a wider lens, to hold the gel.

CT Lee filter

V. Post

Imho, the image outside the window is too well exposed on the second image, this looks a bit fake. Probably you need to "overexpose" it just a bit more.

The additional images probably need some masking I would first try only some gradients to mask them, to make the transition between photos smoother.

And keep exploring HDRI merge.

VI. On the flashlights, prefer uniformity over exposure.

If you feel that you need to put lights closer to an area because they are not powerful enough, don't.

You can compensate for that shot using curves or adjusting the exposure on the post. You have some room to do it using RAW files. But the falloff produced by a close light is harder to work with.

VII. Dark furniture.

I would forget about it. If the walls around them look ok, the shot of that zone is ok. Only in very specific cases, I would put some additional light there.

VIII. One more thing is to determine how much you want to emphasize the artificial lights.

I noticed they are on, but probably they need to be brighter. The only way to do this is by exposing it more by lowering the shutter speed. That is another reason to make bracketing even if you are not considering the outdoor lights.

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Reading some of your comments.

1. Do not change the ISO. Stick with the one you have. But if you are ok using ISO 200, and your room is mostly dark, use it instead of ISO 100. You will expose better the room using the lights further away, and for the ambient shots, you can simply increase the shutter speed.

2. Do not use the auto white balance. If you can not balance all the shoots, use daylight and adjust the other shoots in the post or using gels.

3. Most of the gray cards are only useful just to set up the exposure, not the white balance. I prefer using a white paper and underexposing it to set up the gray (or use a color checker). In the case of a dominant white zone, like the room paint, you could use it. But for architectural photography you do not need a perfectly neutral white, a warmer tome is nice. That is why is better to use gels and keep the golden our look.

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One note about bracketing.

It can help you, not only with the difference between outdoor and indoor light, but also as a way to balance the falloff of the lights as you get further away from the window.

Although the framing on this related post is different, it shows how to use two shoots on different layers to balance the exposure. How was this interior room photo lit? Window...Strobes...Both?