I wouldn't personally do hand embroidery while holding a baby. Too much risks with sharp needles! This may not be what you want to hear but I struggled to do my favourite crafts until my baby was a fair bit bigger. Even when she was asleep, I was just too tired to do more than maybe 20 mins at a time, especially something like embroidery which needs a lot of concentration . It's so much easier now and I'm knitting away all the time. In fact, if you don't knit already - that might be a good alternative as it's a lot more "mindless" - easy patterns like blankets and scarfs can be done just watching the telly! Good luck x
Have you tried crafting with baby sleeping on your lap? I don't do much embroidery but I used to do a lot of sewing with my tiny baby, just lying on my lap asleep, on crossed legs so he wouldn't fall