I have 3 year old twins and the subject came up when my wife got pregnant - no not from her, she's always been very supportive of me riding cos she knows that I'm very safe from first hand experience - she's ridden on the back many times. It came from other family who decided it was their business and they quickly learnt that it wasn't
I would say that obviously you have to do what's best for you and your marriage and your baby. This can be a balance but a big part of that is keeping yourself healthy and taking care of yourself - this includes your mental well-being and if you're anything like me or 90% of others here riding is a big part of that. Non-riders tend not to understand this, they think it's like driving a car - they don't understand that when you ride you can't think about much else and that helps to push your problems and worries out of your conscious mind down to your subconscious and this is what de-stresses you. It's therapy.
Having a child is a very big deal and especially as a new parent there is an inordinate amount of stress for both or you. As a father you're not only concerned for the baby but you'll also worry about your wife too - is she recovering, is she getting back to her pre-pregnancy health, is she bonding with the baby, is her mental state ok - post-partum depression is a very real thing and you should read up on it now and talk to your wife about it if you haven't already. It's your job to have her back on this, cos if she gets hit by it, it can be very hard for her to see it herself.
http://www.mayoclinic.org/diseases-conditions/postpartum-depression/basics/definition/con-20029130
Now, all this worry will either wreck your marriage or kill you if you don't take time to yourself and de-stress. Also the psychological effects of having a child can stir up feelings of being tied down, loosing your own life, control etc etc - this can happen even to people that really really want kids as I'm sure you do.
Even though I understand that she's scared and this
request to you is coming from this place it's still not appropriate. What would be more appropriate from her would be if she said something along the lines of being concerned for you're safety on the bike now you have greater responsibility, instead of telling you what to do. I'm not aware of you financial situation but if you're not a lottery winner I'm going to assume that she may also be secretly worried about how she would raise a child if the worst were to happen to you.
I would address her root concerns but showing her that you are taking them seriously - validate them. Take the time to listen to everything she has to say about it and tell her that you have some of the same feelings which I'm sure you do. Let her see you taking time to actually think about what you can do to make yourself safer. Taking a course is a great idea as well as new gear but that can be expensive. I personally don't buy-in to reflective sashes etc as I think they give the rider a false sense of security but they are cheap and make people that know you think you are being safer at least. Another option is to join a club and maybe only ride in a group of 3 or 4. This would be a last resort for me but everyone pay's attention to 3+ motorcycles riding together - it's a gang thing.
I've taught motorcycle safety courses but I'm not your typical safety nut - you won't see be in a full neon jumpsuit. I wear jeans, a leather jacket, good boots, gloves and an open-face helmet every time I ride, minimum. If I were to ride my old Fireblade it would be full-leathers and my race helmet. When the twins came along I did a complete re-evaluation of my gear, riding style, bike etc etc. I chilled out a lot in my riding style and actually I enjoy riding a lot more cos of it but there were times when going for a 30 min ride saved my sanity and my marriage. I also got a big fat life insurance policy too.