Hi there!
First of all, congrats on your impending arrival!
Regarding your little one...Considering that bedtime is a mere hour or so after dinner, I seriously doubt she's actually in need of anything to eat. It's likely that there is another motivation behind her behavior.
Some of the things I was wondering, and you might consider: What are you feeding her at this time? Where is she eating? Are you reinforcing this behavior in some way (extra attention, staying up after the "posted" bedtime, eating something that would be considered a "treat")? Remember, reinforcement can be attention which is postive OR negative...even if you are arguing with her, she has your attention.
You mention her "insisting" that she have food before bed, which leads me to believe that you are simply not standing your ground. She's 4, you're the mom. Say no and stick to your guns. You have nothing to feel guilty about. She just finished eating an hour or so ago...it's simply not physiologically feasable that she NEEDS to eat that soon after a full meal. Eating in order to go to sleep is an unhealthy habit to allow her to get used to. It also makes for less restful sleep.
If you simply can't get over the guilt you feel when you send her to bed crying because you haven't given in, you might try an alternative: A SMALL (4-6oz) cup of warmed milk in a cup (add a pinch of cinnamon or nutmeg for a more palatable flavor), or a small cup of warm chamomile tea (sweeten with Splenda).
Milk contains tryptophan, the same stuff found in Turkey that makes us so tired. It's also filling. Chamomile is a completely safe herb which smells and tastes good, and has claming properties. These are nice things to add to the bedtime routine which will help to relax her, unlike giving her food, which can wind her up. When using these alternatives, to avoid argument, I suggest making those her only choices. No foods, just one of those warm drinks. If she doesn't like that, she gets nothing at all.
EDIT: In response to those who state that eating before bed is healthy: Upon waking in the morning your metabolism kicks into gear and you eat breakfast. Your body is burning energy at its highest rate. This is why kids need a mid-morning and afternoon snack. But throughout the day, the body's metabolism slows down in preparation for another sleep cycle. When you eat at night your body does not fully "sleep" because it's busy digesting that later snack...which it does more slowly due to the slower night time metabolic rate.
Our bodies are not designed to eat at bedtime. To do so is NOT healthy and will cause sleep problems such as nightmares and other disturbances.
Research to support this: http://www.mta75.org/curriculum/english/effects/eating.html
Good luck!!!