He is being unpredictable and vague about seeing the children because his priority now is his new woman. He now needs to work things around her and to signal to her that she comes first. He will make the appearance of wanting to see his children but if she makes him a better offer then he'll take it every time. Yes it all starts with making a big fuss about 50-50 contact but will quickly diminish. He couldn't even be bothered to make it round last night.
He will be minimising their role in his life to her so he appears more desirable and free. Hence bagging up the chn's things in the boot. She'll know they exist but 'out of sight, out of mind.'
Meanwhile, he will happily blame you for the fact he's not seeing them. He will claim you're making things difficult. This is his brain's way of excusing his behaviour to himself and enabling the selfishness. This self-centredness, where he makes himself the priority, is characteristic of those in the infatuation stage of their affair. However, if he is ordinarily a fairly decent person then there's a good chance he will one day look back in shame at his behaviour towards his children at this point. Which is no comfort now I know.
It's really important for you now to start unlearning all those negative things he has been putting on you recently. All the crap he's been spouting are distractions / deflections / justifications etc to excuse to himself what he is doing. He can't hold himself responsible for doing something so awful as cheating on his wife and children so instead he will need to blame something else - your relationship, you, even your children. Anything he can possibly use - however minor - will be thrown out there by him. Don't let him play with your mind. He will not be reasonable to deal with for a while. His logic and thinking is twisted. He won't see that - it sounds like his mother also doesn't see that (and she's been through what you have!) - but it's vital that you see that. Try not to question where you went wrong; you couldn't have stopped this. Try not to make excuses; it's not a mid-life crisis, PND, regret at a second baby. He's simply had his head turned.
Do NOT allow him to make you feel bad about breastfeeding your baby! You are doing what your body is designed to. You do not need to get your baby on a bottle (of expressed milk or otherwise) for HIS convenience. Breastfeeding is just one part of attending to a baby's needs. There are hundreds of ways of being close to them and building a bond. As the baby gets older she can longer without milk so it's not an obstacle to seeing her. But it is a convenient excuse for why he can't. And another ready-made reason to blame you.
And I know you said you didn't find speculation helpful so I will just say this - sleeping at the office? 😒He bloody ha. Please take everything he claims with a massive pinch of salt. His mother might buy it all but you don't need to.
Please take care and let your parents help. I know it hurts more than you ever thought possible right now but it will get better. You will be fine, your children will be fine. Good luck. 💐