From your 3rd picture the home looks higher than the street?

I would agree, and you even have a lip on the driveway apron.

The third picture is taken across the street and the view is distorted as a result. The street is in fact higher than the home. Short of repaving the entire driveway, are there any solutions to the pooling effect after rains? I've considered installing a trench/linear drain in the driveway but then a pump would also need to be put in to push the water up and out into the street since the elevation gets higher away from the house. Besides this option, are there any others?

Can you show us exactly where the water pools and does it actually enter the house or garage

What other options are there for where to send the water besides out on the street? We were trying to avoid installing a pump, but not sure how else to get rid of the water.

@Karen Roan you are wise to address this aggressively. I had the reverse problem with a driveway with three grades, one of which was dangerously steep when ice or snow covered. I removed the driveway and had it regraded to solve the problem. I wonder, since yours is cracked, if that might open a path to a solution other than using a pump. In a storm with heavy rains the power can go out. 

If you DO remove and regrade your current driveway that is an excellent time to have a plumber scope your main home drain line if it is located under the driveway. If it is badly clogged or broken, prepare to replace it when you remove the driveway and before the next one is poured. 

Also, if you have to replace your driveway, expensive, spend a couple thousand more to install radiant heating under it (electric works fine but if you have gas you could run that type). No more shoveling and no more ice storm worries. We love ours. So nice in our golden years to not have to worry about that headache.

You don't have to send the water uphill to the street.

Install a drain near the garage door, extend the pipe to the left with an 18 inch deep and wide trench filled with rock, gravel into the landscaping.

Yes you need to cut up the driveway..... but you won't need a pump.

Basically ....... like a french drain. The left landscaping appears to already slope downward a bit.

The pipe outlet on a trench drain just needs somewhere lower for it to send the water to.

- If there is any slope down anywhere to the lot, it can be piped there to daylight on top of grade.

- If you have no slope but have room, you can dig a broad detention area lower than the pipe and daylight into a sodded or landscaped basin.

- If you can size it for a worse case saturated ground scenario, you can install a drywell(s) for the pipe to dump to (looks like Florida, so even with deluges of water, sandy soil drains fairly rapidly). If you were to use a pump, you would need a detention basin (drywell) anyway.

- Demo'ing and raising the apron to block water from entering from the street. This would not address water collecting on your side of the curb.

- Making sure the storm basins in the street are clear so that water flowing down the street does not back up.

We live on a hill and while our driveway is fortunately graded down to the street, our backyard paths are not. The previous owner put in a drainage system with a trench drain at the low point of the back paths that feeds into a pipe that runs the length of the driveway down to the street and spills into the municipal storm drain. It's not the prettiest--they had to cut a trench through both the 100-year old garage floor and driveway to get the slope needed to carry the water out--but it works well. I will say that I live somewhere where it never freezes so the biggest issue we've had has been that street sweepers sometimes clog the end of the pipe with debris at the street. YMMV if you have real winter and issues with snow melt, ice, etc.

Has anyone noticed the drain in the driveway?

To the OP, is the drain clear?

I noticed the drain...... too small : ) too far from garage doors, as well.

Water only flows downhill. If there's no place to drain it, you can create a rain garden, which is environmentally beneficial.

install french drain at the bottom of driveway slope.

As others have stated, you'll want a trench drain running across the driveway and possibly field drains anywhere in the yard where you're getting standing water. All of these, of course, plumbed with schedule 40 and in a graded run away from the problem area(s). Pretty simple and easy to accomplish. You should have a number of local contractors who can handle that for you.

Good luck!