As the Commando, how can I effectively combat large groups of children?

Success in risk of rain is mostly based on three parts:

Learn to play your class

You must learn to play your class very well and need to know, when you can stand against an enemy or when it's better to back off and/or kite. Just play some random rounds, not with the aim to complete the game, but more to test all your abilities. In your case for the Commando you need to use your roll and knockback skills in the most efficent way. So dive through big amounts of enemies to get a bit away, then fire your knockback into them and back up more. Use your primary attack from far away, to get constant damage on your opponents.

Know what you need to buy

For this part you should already mastered part one, so that you know weakness and strength of your class. As you mentioned in your question, you're uncomfortable with your knockback. So save some money and buy wisely. Some Boxing Gloves will increase your knockback for 15%, which is very nice and stacks. If you manage to get 3-5 of those you will knock enemies out of your viewdistance. Keep in mind that there won't be a perfect build for any class, because everyone plays a bit different. I would say you need to go for knockback, hp regen (per kill, nugget and out of combat if you want) and of cource damage.

Be lucky

As in any games where you need to get itemdrops you need to be lucky. You can be a master at your class, but when you just get garbage, you won't be as good as you could be. I can play one run for 2 hours and lose the next try after 5-10 minutes. To extend your luck keep an eye for 56 Leaf Clover. This dropchance-booster helps a lot to get better loot and can turn the table in a round with bad drops.

secret 4th part - active item

The secret 4th part to success is your active item! Read about them in the wiki and try to find the one which fits your class and playstyle the most. So I used the Instant Minefield a lot. With some good damageboosters and evation-skills (like your roll) you can nearly oneshot champions. This party is totally up to you, but there are some very crappy active items. One of the strongest of those - based on my knowledge - is Jar of Souls. This will help to smash so many enemies on the map, but be careful. Jar of Souls can drop your Frames below 10 in the later (farm-)stages.