No need to take another reading with your extract kit. You can pretty much trust your directions for the OG.
I had lots of issues with weird readings from extracts, both due to my own stupidity as I was learning and the very real problem of mixing sugary liquids properly. It can be baffling when it doesn't mix. Now if I am using extract, I simply trust the math. There is almost no way that the contents of the can are off by very much, so if you know how much volume of water you add, you can use an equation.
I add up the total points in the can (liquid malt is about 36 points per pound per gallon, so a 3.3 lb extract can contains ~118.8 points per gallon).
I divide the total points by number of gallons water added (I like to put one can into 2.5 g
water, so 118.8/2.5 = 47.5 points, or an OG of 1.047-1.048. If you put it into 3 gallons of water, you will get an OG of 1.039-1.040. You can reliably add dry malt extract or sugar by weight to fine tune things from there, such as bringing up 3 gallons into the 1.045 range if you wanted to.)
In the front of my brewing notebook I copied the points per gallon of common ingredients so I can reference them easily. This helps me estimate any steeping grains, extracts, or other things I might add.
Try not to stress accuracy tooo much. Like exactly how much the steeping grains add. Feel free to think in intervals of 5 (5 points, 0.5% alcohol, etc.)
When accurate gravity reading really really matters is when you bottle. Make sure that the fermentation is complete and don't be satisfied with a reading that is relatively steady. 2 gravity points of unfermented sugars are enough to create bottle bombs. The good news is you can always just let beer sit for another week or two if unsure, and 90% of the time you get better beer for your patience anyway, so it's a win win.