Yes, I developed rosacea when my daughter was probably 4-5 months old. I never had any problems with it before, so I always did assume it had something to do with pregnancy triggering it. Pregnancy can trigger auto-immune conditions (like lupus), and there are some theories that rosacea is an auto-immune condition. My daughter is now 2.5, so it's been 2 years since I first got it, and it's pretty much in remission now and has been for nearly a year. I can tell you what I did that I think helped.
(1) I did do 2, maybe 3 courses of antibiotics at times when I had a really bad flare up. I also had ocular rosacea, which is like rosacea of the eye, red, watery eyes, that got crusty, much like conjunctivis, but not. So I did a course of antibiotic cream to the eye as well. That helped to quickly reduce the inflammation. The reason for the antibiotics is not because of a bacterial infection, but because antibiotics are really strong anti-inflammatories and rosacea is an inflammatory condition. So when it was really bad, that helped to bring down the inflammation so I could get on top of it with other things. The last time I had to use antibiotics was probably last July.
(2) I just generally tried to reduce stress and inflammation in my life. I took a probiotic, which is supposed to help sort out any gut issues, which could be related to triggering rosacea. I also took tumeric capsules (you can buy them in Holland and Barrett, or make your own from ground tumeric). Tumeric is a powerful anti-inflammatory. I also really tried to reduce stress and get more sleep. Mine started when I was just under a lot of stress and not getting much sleep. It would always flare up on a particularly stressful day. Do whatever you need to do to reduce stress (exercise in the evenings once your LO is in bed, plan a spa day to yourself, force yourself to leave the dishes and go to bed early 3 nights a week, whatever it takes).
(3) I also changed the products I use on my face, and I think this is a big part in why it's been in remission for so long now. I stopped using soap or any sort of synthetic moisturiser or whatever on my face. I started doing the oil cleansing method once a day before bed and that's it. I don't wash my face with soap or do anything with it in the morning. I've always had oily, acne prone skin that had a tendency to get dry and irritated in patches. Oil cleansing has been like magic! I recommend it to everyone. I use a blend of 1/3 castor oil and 2/3 sweet almond oil, plus a few drops of lavender and tea tree essential oil. When my skin was really inflamed in the beginning, I also did a oat scrub in the mornings too for a few weeks til things calmed down (basically, it's fine milled porridge oats, mixed with a bit of warm water to make a paste, rub on face, let it sit for a few minutes, wash off). That helped a lot with redness and irritation at the start. I don't do it really anymore though, just oil cleansing, and now that my skin is okay again, I apply a Weleda moisturiser at night before bed. I've been doing oil cleansing for a year and a half now, and it was a few months after I started that I needed by last course of antibiotics and since them have been fine, so I think surely the two must be connected in some way.
Here is info on the oil cleansing method: https://wellnessmama.com/7569/oil-cleansing-method/