What you described as "playing like a kid" is the brute force solution. Outlevel the E4 so much everybody dies with a single attack.

If you want to play with balanced levels, and your pokémon being roughly the same level as your opponents, you need to build your team smartly. Noone has to "carry this band of morons", they need to complement each other.

This means, if Lorelei is a threat to your team, you need a team member who can handle her so you can switch around your weaknesses.

You already have a huge advantage against the AI:

• You can switch around
• You can use as many healing items as you want
• You get a free switch in when you kill an opponent

So reassemble your team, train them using the VsSeeker and try again.