On maternity leave, I went for at least one long walk each day with the pram for between 60 and 90 minutes, sometimes longer. I used to pack a flask and stop on a bench in the middle of the walk for a cup of coffee. As we didn´t (and don´t) have a car, I used to walk everywhere else I needed to go to (or catch public transport...getting the pram on and off buses and trains is a serious workout!)
With my second child I had a three year old as well and I used to take him to the park to run around each day and for "bike" rides and swimming at weekends (with my husband so we could take turns having a proper swim while the other played with the children in the pool).
I was ravenously hungry after both births but found I was satisfied by eating huge quantities of fruit and, particularly, vegetables, as well as plenty of protein.
I think it´s key to try and get some routine with things like your own eating and, if you can, sleeping as overall you will have more energy and generally feel more in control of what is a busy and even stressful time.
You mention some health problems so exercising may not be much of an option for you; perhaps focus on some healthy meals that all of the family enjoys and, if you have time before the birth, make some in batches and freeze them. Also consider switching to having your groceries delivered so that you know you will always have a supply of your favourite healthy foods even when you are too busy or exhausted to get out to the shops.