Firstly, this is not on you, or the dog, or his ex. The responsibility to sort this out like an adult sits squarely with your DP.
There are plenty of ways to improve this situation, all fairly easily, for both you and the dog. ALL of them need him to get off his arse and do something rather than placating you with, it will sort itself out. It will if you leave it long enough, and it won't be pretty because you will lose your shit quite rightly when you've got this to deal with and a newborn. It's not fair of him to let his pregnant partner become stressed out about something and continue to ignore it.
He needs a massive kick up the arse, let him know that you have come up with a plan, and it's his responsibility to sort out the dog walker, (I think doggy daycare would be more suitable as ten hours is too long for a dog to be on it's own even with a walk), the rug, the routine etc, and you'll give it xx amount of time.
An 8 year old terrier is likely to spend a fair amount of time in kennels in rescue, they're inundated at the moment, so get him to step up and make that a last resort. This is fixable.