For reference here and because it may change, the circuit you are currently asking about is:
This is supposed to regulate output current, but the complaint is that it is unstable. R1 is meant to be a high side current sense resistor. You say this is for charging 12 V lead acid batteries. You don't say what current, but probably a few amps. In that case 100 mΩ seems rather large. Note that at 5 A it will dissipate 2.5 W.
However, the large current sense resistor should only make measuring the current easier. It looks like your intent is that OA2 provide a ground-referenced voltage proportional to the current thru R1. That concept is good, but the implementation is flawed.
What you need is a "diff amp" that has some finite gain. The differential part eliminates the common mode voltage on R1, but the finite gain part is also important. As it is now, OA2 is being used open loop as a comparator. It's output will quickly switch between full high and full low as the current goes slightly above and below the regulation threshold.
Another problem is that the top of M3 is not connected anywhere, so it can't source any current onto R7. I don't know what that dashed line is supposed to show. Usually if things are connected to it like that it means a conductive case, but you show nothing else connected to it. A case is usually grounded, which is certainly not what you want the source of M3 (strange designator for a FET) connected to. It also makes no sense that you need to buffer the output of OA2 amplifier. I didn't look up a LM358, but if that does not have a push pull output stage, get one that does.
All in all, I'd lose the wierd current sense amp circuit as it is now. There are diff amp chips that do what you want directly. Sometimes they are called instrumentation amplifiers. These have a truly differential input, finite and sometimes adjustable gain, and the output can be referenced to some other voltage like ground.
Once you have a reasonable ground-referenced voltage proportional to the output current, you can feed it into the negative input of OA1 as shown. However, you have to make sure that the controller (OA1 in this case) is slower than everything else in the system. I mentioned this already in another one of your questions. Put a cap between the output and the negative input of OA1 to slow it down. This may require a resistor between the current sense amplifier output and the negative input of OA1 so that the cap has some impedance to work against. Do not under any circumstances attempt to slow down the current sense circuit. That will only make things worse.
You will never get the ac and dc performance with the Wilson current mirror that the Howland current source can attain. Plus the Howland can sink and source current.
For the Wilson current pump, consider the mirroring BJT's constant current region - there is a voltage on the base set by the "other" BJT (that is acting like a diode) and you know that this sets a current into the base of both transistors - look how compliant the graph is - outside the saturation region. It's not really a good constant current source when Vce changes: -
The Howland current pump (on the other hand will have a compliance graph that is as flat as a pancake meaning you can swish Vce around and the collector current will remain really quite flat (dependent on resistor matching of course).
Best Answer
Current sense amplifiers are designed to operate from a low source impedance, so they can have lower input impedance than opamps, which allows topologies that offer features not available to opamps.
Among these the most interesting is the ability to operate with input voltages way beyond the power rails of the amplifier. This is extremely useful for high-side current sense.
You also get convenience and cost features, like having good offset and CMRR without having to buy expensive matched precision resistors.
These features are very useful for a high-side current sense, but not for a low-side current sense. In low-side, you don't have much common mode so CMRR is not that important, and input voltage is close to ground, so you don't need an amp that can take inputs beyond the rails.