First, congratulations on your baby girl. Yes, you can co-wash on relaxed hair. The object of co-washing is to avoid the sulfates found in regular shampoos. However, you can now find loads of shampoos (organic). Curls, Kinky Curly, Donna Marie, Hydratherma, all have products that fit the bill! They are safe and effectively and thoroughly washes relaxed or natural tresses. The drawback is that oftentimes they will not suds up like sulfated shampoos.
You can transition your relaxed hair to a full head of natural tresses without the big chop! In order to do so, you will need to adopt styles that will allow you to successful do this. Twists, flat twists, braids, bantu knots, and even slicked back pony tails will work for a period of time.
I wouldn't suggest putting any "chemicals" in or on my head. Research your "natural relaxer" carefully they should be chemically-free and organic. Some people have seen improvement over a LONG period of time.
I took the road that your sister did. I tried to transition for over 6 months but got tired of dealing with the two textures on a consistent basis.
However, another option is to keep your hair braided while wearing a wig. I'm not a big fan of weaves because you can't as freely monitor, wash, and refresh your natural hair as needed.
I hope this helps and best wishes to your new baby, your sister and yourself!