Lots of parents either don't drive or don't have cars, but they manage to get their dc to school every day.
'Custody' has been replaced by child care arrangements orders which can be negotiated as part of the divorce process. It's unlikely he'd get more than contact every other weekend with the dc he has with you and, regardless of what he may threaten, the chances are he won't want to be encumbered with a dc especially when you tell him that you'll be using the time he has his dc to go clubbing get out and about and meet om with friends.
If you're worried about how you'll manage financially others here can tell you what you'll be entitled to claim such as housing benefit, tax credits, and child maintenance.
In short, none of the reasons you've advanced so far are cause for you to continue this marriage and the effect it's having on you and, more especially, your 7yo ds is every reason to end it asap.
Fwiw, your ds doesn't sound any different to thousands of other dc who are living with a stepfather who makes a marked distinction between them and their half-siblings. Your little boy doesn't have the vocabulary to tell you how he feels and and refusing to comply with whatever requests are made of him is his only way of expressing and relieving his feelings and of course he's angry with you - you bought this man, who is unkind to him, into his life and had another dc who takes your attention away from him.
If you have family members who will stand shoulder to shoulder with you and prevail on your h to leave, PLEASE solicit their help asap. I'm not an alarmist but I would caution you against attempting to make him leave without some back up in the form of irate dps and/or hefty male. family members.
I suspect that what you've said here about your h is merely the tip of an iceberg of abuse with gaslighting being the very least of it. You and both of your dc deserve so much more than this and I suggest you make contact with Women's Aid and begin to get his behaviour towards you documented as a matter of urgency. www.womensaid.org.uk