I don't think it's unreasonable to not want custody/be the primary carer or whatever the current name for it is. Each to their own. People will judge you for it, it's whether or not that judgement will affect you from a depression perspective that you should consider and take steps to get help for your mental health if that's appropriate.
OP you've said that you have a new job, which has good prospects for career advancement but is currently not particularly well paid. Difficult to know if you mean £10k or £35k though so I'll assume it is enough to live on without too many luxuries. From a practical perspective have you considered how you will fund a home closer to the city [usually at a higher price] which is appropriate to take your two children to at the weekend? How you will manage transport costs etc?
If you have only just gone back to work, I would personally give it some time before taking off to the city. I don't underestimate the sheer euphoria of escaping the often drudgery of being a SAHP but its a huge adjustment for your children to make, to so quickly to move to only seeing you two days a week?
Or is there more at play here? Are you just married to a controlling twerp who you want to escape from at any costs. Remember, you might not be the Mum of the Year by whatever set of criteria you hold yourself to, but your kids still love you.
There are plenty of us on MN who would do anything to avoid a mother and baby group, have zero interest in home craft activities and automatically schedule in Cbeebies just to have a shower in peace without WWII kicking off. I couldn't wait to get back to work and while there's the odd day, mostly I wouldn't consider being a SAHP. If DH is away, I often feel suffocated at the lack of headspace and dream of a cottage in the country just for me for the weekend.
What you are proposing is unusual and a lot of the comments above have inferred that its off the back of PND and something you might regret later. For your own sake, I would try to give yourself a bit more time to settle back in at work, whether your marriage is irretrievably broken down or not, and consider a 50:50 arrangement for a while to assess if it works for you and your children.