Hi Becky,
Congradulations on the little buns :>
I won't pretend to understand what it's like being a woman, pregnant, or having to look after a little girl whilst losing weight
But i will say that not eating isn't the answer, i'm sure you know this. The solution is obviously to eat, find a whole range of healthy foods which you enjoy/might enjoy and keep them stocked regularly
Don't dip into junk foods or snacks, plan your days so if you get hungry there's a piece of fruit or sandwhich you can eat if you're out and about, keep a bottle of water handy
I'm not an expert on eating healthy during pregnancy and definitely recommend both self studying and asking for help/advice from other mums and your doctor

knowledge is power when it comes to your diet
For excercise i'd recommend looking into strengthening key areas, legs and back(lower back) spring to mind when thinking about your situation.
Again i'm no expert but recommend going to one and finding a range of excercises to suit your needs, focus not onto one excercises which help during pregnancy but also excercising to strengthen key areas you need support in
As an example, my lower back and right knee both have old injuries and are focused areas for pain and problems, i work targetted excercises to stregthen these areas and the support areas which help take the weight off them and relax and do lots of simple balance excercises to keep me stable and help prevent injury
Good lucky with the new baby, trust that there are others who understand what you're going through