I take it you know how Brood works right? She's the queen of split pushing. She never leaves whatever lane she chose no matter what. Your team needs to constantly distract the enemy and / or push lanes while you concentrate on your one single lane. That kind of thing. If you know that part, then I'll share some tips on how I handle the early levels with Brood.
---------
1. It's generally a very good idea to grab an early soul ring. How most people do it is to either grab the whole thing in one go if you randomed her, or grab the recipe and whatever else you need. After you get enough gold you can buy the rest of the components at the side shop (which should be pretty fast honestly). The reason for this is that Brood is an incredible lane bully. Once she gets her soul ring, the lane is basically won. You can imagine her Q as the same thing as Phantom Lancer's spirit lance. Except Brood has amazing regen in her webs so the spam will never end. None of those heroes you mentioned there will be able to touch you. After all, when your Q does 1/4th of their hp each time you use it... what are they going to do? They can't even reach you to retaliate, the range on it is so freaking long.
2. Tangos are vital for the first 3 levels. Brood has a giant target sign on her back every time she appears from invisibility to grab a last hit and the enemy laners WILL autoattack her when she comes out. At about level 5 or so you can start ignoring this damage since you'll have your Soul Ring and level 2 webs (7hp/s herp derp), but before then you can't really handle the damage well. The only other alternative to tangos is to not autoattack until level 5 so.... grab tangos.
3. Grab a quelling blade if you can afford it. The reason I recommend this is because Brood has kinda low-ish attack damage and she relies a lot of standing at weird positions in her web before scuttling in and nabbing quick last hits. Doesn't really work if the base leeway for the last hit is too low. It'll just give you a way easier time overall and I would say it's mandatory if going up 1v2 as you need to have way more attack damage than both your opponents to stand a chance.
4. Generally, what you want to do is clear out as many trees as possible with your initial webs. Then hide at weird spots and keep an eye out for sentries. Never sit in the creep wave. The best locations would be behind the enemy or off at the side. Behind the enemy is good as they normally can't turn around fast enough (dota 2 has weird turning speeds) to retaliate if you attack them before you go invisible again. Take maximum advantage of the invisibility and do as you please in the lane. Yes, she's definitely a carry and is much weaker for the first 3 levels or so (protip: one of the stupidest things I've done with her is 1v1 Axe at level 1). But once you reach level 4 with two levels in Q you should start getting super aggressive. At this point you should have your soul ring too. Spam that Q. If the enemy is even 1cm out of position start smacking him with the web poison. Things like that.
5. Never, EVER, use your spiderlings to do anything in lane while the enemy is still there. Send them to farm the jungle. To make the micro easier, change the keybinding for "select all controlled units" to something like "x" and constantly send all your spiderlings elsewhere. They actually give quite a lot of gold and exp, especially in the numbers Brood tends to spawn them. Once the enemy leaves the lane then you can use them to push down the tower. The side benefit of doing this is that you yourself will gain gold and a much more rapid rate (though I'm not too sure about the exp).
6. Take advantage of your high regen. Aggressive is good. Especially if you can accurately judge how much damage you will take each time you trade. As long as you're inside your web, you should be baller to the max and show the enemy who's boss. I have not found anyone other than a Phantom Lancer with KotL to support him that can output the same level of spam as Broodmother. Remember, the goal is to chase them out of the lane and gain a massive exp advantage. Doesn't really matter if you kill them or not, if they run away you did your job.