Hello @waffles1990 - amazing that you are considering fostering! In terms of DH's health, my thoughts would be as an assessor that presumably he plays a big role in the day to day care of your children, and therefore he is already demonstrating that he can meet children's needs - i would obviously be guided by the views of the medical advisor however.
One thing you will need to consider is the driving aspect, very young children often have contact with birth family several times a week, the expectation is on foster carers to transport for the most part. You could probably negotiate this in terms of when you are available to do the driving however, and the LA may be willing to provide some support with this. The same applies with older children and school runs - LA's try and maintain schools where possible which means you may be caring for children who don't go to school locally.
Lastly, certainly have conversations with Local Authorities, different providers etc, i would imagine that you will be advised that 0-2 is very restrictive - you are doing the right thing going down the LA route if you only want to foster younger children but even their approval categories by age tend to be 0-5. They might try and persuade you to be more flexible as they have the most need for foster carers for older children.
Hope all this is helpful, give me a shout if you want any further advice.