Wow, that's a lot of work ahead of you. Even if the stripper worked perfectly, you have to get _it_ out of all the carvings and details, and then you have to be careful with them when you sand, stain and finish. I looked at a set _very_ similar to this a couple of years ago (Was it you????) and declined the job due to the amount of hand-work making it impractical.

Pine is never going to look like mahogany. The "casual" form of this piece is also inconsistent with the formal finish on the mahogany pieces.

Have you considered either a glaze or black paint?

Well, it might have been me, if you're the guy who does the custom touch-up work for Branch Cabinetry (and if it IS you, I'll be calling you very soon for different work for us here).
I'm not aiming for my the antique pieces to match or even look like mahogany. . . just much darker would be a good start. I'd already thought about using Minwax's Gel Stain, but was then told it would chip off too easily on a dining room table and chairs that are used every day. Same with black paint. If you can tell me a way to avoid the chips, I'm ready and willing to go that route instead. No one is going to want to buy this set from me in it's present condition, even though it's wonderfully carved and made well. And, it looks too odd for us to keep it as is with the new antique pieces. I'd love to go with an antiqued black look. Any ideas now???

That is the ugliest finish I have ever seen on southwestern style furniture. It looks like wall paint. I used to work for a southwestern furnishing company in the 90's and we never painted anything like that.

All I can suggest is Jasco paint and epoxy remover and lots of steel wool. A sharp narrow chisel can help scrape out the inside detail. Hold the chisel straight up and drag the blade against the wood, scraping away the surface- but it won't gouge if you hold the handle straight up in the air and scrape toward you.

have you looked into having it stripped professionally?

It's not a solid white "paint" that I see on that...it's more fo a wash....
Does it have to be solid black? Or solid brown?
I would take a mix of laquer thinner and shellac thinner...the proportions vary according to your finish and just sop it on and wipe off the old finish. I wouldn't attempt to strip it clean....but just to get some of the white off.....then wipe it with a very dark stain....the tone of which depends on what you want.
I wouldn't attempt to make it a "painted" set but rather darken it so it blends a bit more with your antiques and gives your room an ectlectic look rather than mis-matched.
Linda C

"take a mix of laquer [sic] thinner and shellac thinner"???
I'd do a little testing before proceeding with this. It would work on some finishes, but not others.

The only finish I have found that it doesn't work on is latex paint or milk paint...
But I agree, test a spot to see if you are getting white on your rag.