>>Will I be expected to pay towards the mortgage as well as paying my own rent?
No, absolutely not. He has the benefit of living there and you do not. The mortgage can be treated as the equivalent of rent. If he cuts up rough about this you can point out that he is living in a property half owned by you so you expect him to pay you an occupation rent for using your share of the property.
You should stick to your guns on getting a fair share of the equity. Since you have the care of dependent children there is no good reason why he should have more of the equity than you and there may well be good reasons why you should be entitled to more than half (although this does depend on the figures).