And I'd like a toilet made of solid gold... but it's not in the cards, baby.
With the exception of grills that use a small gas burner to start charcoal as the main fuel, I have seen no "duel fuel" grill worth having. Charcoal is successful when it exposes the food directly to the fuel. Gas is successful when it isolates the food from the fuel. You can't do both.
Throw in a desire for portable... and then ask for under $100, and there isn't a decent-quality grill that meets your needs.
I have has the same Weber gas grill for about ten years now. It looks almost new and it functions perfectly. It clearly has years of use left in it. Yes, it did cost $1100. Meanwhile, every spring -- it should be any day now -- my neighbor behind me buys a new grill for $150ish and brags to me about what a great deal he got and all the great features and accessories and everything. About mid-summer, as I'm grilling up another mouth-watering meal, I'll see him (usually waving his hands trying to put out some conflagration) and ask, "How's that new grill working out for you?" and he'll say, "I just can't get the hang of it." When it comes time to clean up for winter, that new grill will be set out for recycling ($20 pickup fee) having made exactly zero excellent meals.
My strong advise is bite the bullet (so you can bite into a great steak later) and invest in a $500 Weber Genesis. It will last you for many years and make you many delicious meals.
Buy quality and you only cry once.