Hi Neel, I am sad to read your post. Your son loves you so much and yet you are feeling so underconfident.
I have a few ideas;
Have you tried divide and rule approach? Get your MIL and talk to her about how your DH is ruining your confidence - and vice versa. Then see if anything improves.
Secondly, you are the boy's mum, and you can look after him perfectly well, if not better than anyone. No-one is perfect and if he falls over a bit more when you are there, then maybe it's because you aren't supervising him and hanging over him the whole time - and I think that's a GOOD thing, cause babies love to explore and be independent.
Thirdly, put yourself in charge. It sounds as if you are feeling third in line to your son's care, and this isn't right. You're his mum and you're the BEST person placed to look after him. Is the arrangement agreeing with you working full time? Do you have to? Would it be possibly for your son go to nursery a few days instead to adjust the balance? Maybe going on holiday is a good idea at least so that you can get some confidence back that you are a good mum. Obviously you will take good care of him and chances are he won't have a terrible accident.
I know how hard it is to sit down and talk about all these things especially when you're trying not to rock the boat, but get friends involved and try and mention a few things to your partner. He mustn't make you feel shit about yourself, your baby or your arrangement.
Lastly, see if you can laugh the thing off with your DH ... I'm always having accidents with my babies. I am a bit absent minded, but I like to say that my kids are nice and relaxed when I am around, as I do not jump whenever they are in danger. I wait a bit (if I notice haha). My DH always says I should take more care and I try and laugh about it, saying not everyone can be as perfect as him! If he went on about it too much, I'd have a go.
Be strong. You are number one!