This is so sad (if it's true).
It sounds to me like the dad (OPs partner) is going to work to support his blended family. The mother (dad's ex) is also working, presumably to provide for her 2 children.
The OP is a SAHM with her "own" 2 young children, is finding parenting them hard (not sleeping properly etc) and her partner is expecting her to care occasionally for his 2 older children in his/their home.
I am really not understanding the problem here. Did Mallodie really not stop to think when she hooked up with a man with 2 children that she may be expected to assist in the care of his children? Surely as a stepmum they are by extension her children too? They are the half siblings of her own children for goodness sakes!
Mallodie - you need a reality check. Children do not stop needing care and supervision once they hit 10. They are still children. You cannot expect them to live over the road in an empty house for the day whilst you swan around with your little ones.
OK I can understand you might be feeling out upon, but you need to sort that out with your partner not take it out on 2 rather abandoned children. Ignoring them and not feeding them is petty and childish, even more so if the older one has special needs. You should be more helpful in his case, not less so.
I don't think you're depressed and I don't think you need to see a GP, but you need a kick up the bum to realise that you have a very skewed view of parenting especially in a blended family. You're all in this together and the sooner you sit down with your partner and get it sorted the better really.