Chilean Mesquites make great shade trees. Yours should grow at a moderate rate and mature to a size of 30 ft. x 30 ft.

Mesquites can tolerate growing in a lawn situation although it isn't ideal. The water needs of your lawn are drastically different than the trees. While lawns usually need water twice a week in the summer, an established mesquite only needs water once every three weeks or so. The amount of water applied is different also. Grass only needs water to moisten the top 6 - 8 inches, while trees need water down to three feet.

To compromise, be sure to deep water your trees periodically either with a hose or drip system. Eventually the shade from the trees will cause the grass to become sparce. Even shade-tolerant grasses will struggle under the trees. When this happens you may want to cap off the sprinklers under the tree and use a shredded bark mulch to cover the bare soil.

Don't prune newly planted trees, except to remove broken or dead branches. Wait for at least one year to do any pruning - early June is the best time, but minor trimming can be done at other times. It is normal for mesquite branches to droop to the ground. On the branch you mention, try working from the tip of the branch back and remove a shoot where it intersects with another branch or shoot. This will lighten the weight on the end of the branch.

As far as staking goes, be sure to remove the original nursery stake that is next to the trunk and replace it with two wooden stakes placed outside the rootball. Allow the trunk to move a bit within the ties. This creates strong wood in the trunk. The ties should not cut or bruise the trunk - old pieces of hose with a wire inside are great or you can purchase ties. Your goal will be to remove the stakes in about a year.

More information on pruning and staking can be found in the book Pruning, Planting and Care by Eric Johnson, Ironwood Press. It's available in local bookstores or on-line.

Another great book is Desert Landscaping for Beginners by the U of A Master Gardener Press. It has a chapter on pruning, one on watering, one on turf care, citrus, roses, cactus, landscaping for wildlife, etc. I've included the link below.

I hope this helps.

aztreelvr
certified arborist

Here is a link that might be useful: Desert Landscaping for Beginners