baby catalpa trees growing everywhere

Disclaimer: this is probably a stupid question.  But I'm a newbie.  Be nice.

We have catalpa trees in our yard.  Yuck!  I'm not too pleased with them.  If we wanted to spend lots of money, we'd probably get them removed.  But it's not that high of a priority.

Every year, there are tons of new baby catalpa trees growing all over our yard.  I just spent some time this morning pulling a bunch of them out (I finally stopped after I ran into some poison ivy.  Different thread...)  So, is there anything that I can do to make life easier?  How do I prevent all these trees sprouting up?  Or at least, are there suggestions for pulling them out easier?

Related topic: the previous owners DID have one of the trees cut down, but they left the stump.  The crazy thing is still trying to grow!  I chopped off lots of branches from it this morning too!  (Again, I know that the best option is having the stump removed, but I don't want to spend that kind of money...)  How do I get control over the catalpa forest that my yard wants to grow?!?

I take it this is in your lawn?

Does mowing them not work?

Yes, my lawn.  I guess mowing them does work for the ones that are out in the mowable area.  Which, thinking about it, gave me an "ah-ha" moment.  See, there are areas of the yard (by the house & by the fence) that the previous owner separated off for flower gardens.  But, uhhhh, we don't do that.  So, instead, the "garden" areas just grow whatever the heck they want.  And we don't mow it b/c of the separators.  So, I realized: DUH!  We need to remove the separators and just mow that area like the rest of our yard.  B/c the only things growing there now are weeds & unwanted trees.

Also, some grow right up close to the fence.  My husband does the mowing, not me, but I assume that they're just too close to the fence for him to get regularly, so they quickly get too big to mow down.  So it's just been a once-a-year pulling session.  Maybe after I get them all out, I can make a point to him to please try to mow closer to the fence and get everything growing there.