You both clearly have a problem that needs looking into by the medical profession.
Neither of you should be tearing.
When you were having your baby, were you cut and stitched? You may have been too tightly stitched.
I would suggest you do not have penetrative sex until you are both completely healed.
Do not use soaps or shower gels to wash the genitals as this will dry the delicate skin. Use non perfumed soap or a soap that has a pH level like our skin, baby washes should be fine.
The doctor can prescribe a moisturising cream like Dermol 400, Dibrobase, Doublebase, that can also be used as a wash. Dermol 600 is a microbial moisturising solution that is added to the bath water. The doctor may also prescribe a steroid cream to help with the healing.
It may be that you both have a fungal infection and a swab would show if this is the case and a prescription for an antifungal and antibacterial cream would be prescribed. You can buy antifungal creams specifically for the genital area from the pharmacy without a prescription and also Fluconazole which is a single dose oral capsule. I would wait for the advice of your doctor first.
Taking a bath with a couple of handfuls of oats in the water will help to heal the soreness as will applying a natural live yogurt to your cleaned and gently dried genitals. This works for both men and women.
You and your husband may prefer to be referred to a specialist who will be more familiar with these types of problems. You both may have a condition called Lichen Planus. There is no cure for this, but it can be managed.
Wishing you both a speedy recovery so that you can both enjoy a fulfilling and pain free sexual experience.
Can I ask what lubrication you used? You really should use a water based one like KY jelly. Almost all people can use this kind with no problems.
Sorry to hear about your problem. My issues is that you stated he might go elsewhere. I don't know the problem to your issue, but I think there are other ways to "get him off" as you work through this problem. Just make sure you guys are communicating and trying to figure this issue out.