How old is your DS, and is he still in nappies (sorry, but makes an enormous difference in advice)? I'm assuming at this point that the urine samples were clean catches, and showed both white cells in the wee, and growing pure growth of coliform (not a mix of bugs). If they were pad or bag samples, please please please switch to clean catches.
Reasons for young kids having UTIs:
Bad luck
Less than ideal fluid intake (in late toddler/infants is v common problem)
Less than ideal types of fluids (again don't know the age - in older kids often have to ban fizzy drinks and citrus juices)
Hygiene stuff (more in little girls, but can be an issue in boys - ban bubble bath, don't sit in water with shampoo etc, wiping properly after pooing)
Hanging on (stale wee is quite irritating to the bladder, making it more vulnerable to infection, and giving any bugs more time to multiply)
Constipation - major major risk factor. If they're constipated, then the waiting-to-come-out poo, sitting in the last bit of their gut, is squashing up under the bladder. This tips the bladder, making it hard to empty out all the wee, which brings us back to the stale wee problem. Also, the poo hanging around waiting to come out stretches up the anus, tending to leak more bugs onto the skin in the general area - more bugs on the willy, means more chance the odd one might make it to the bladder
Problems with the drainage system (rarer than the other reasons).
The scans:
Ultrasound looks at the size and position of the kidneys, the bladder, and the tubes connecting them together. So it gives information on the structure, but not how things are working. It's a very good start, and usually the first imaging test (and for many children the only test)
DMSA is a sort of dye test. Dye is injected into the veins, the kidneys suck it up to get rid of it, and you take pictures of that happening. This test looks for any scarring/damage (most kids do not have any of this) from the previous water infections. The scan can be done at any age, but is meant to be several months after the most recent infection. If it is done too soon, and it is normal, then the test can be believed. But if it is done too soon, and shows a scar, it might really only be a bit of the kidney that's still recovering. People don't like to do them too soon because of the risk of needing to repeat them if it shows something - it's not a very big dose of radiation, but it's quite a bit more than say a chest xray, so people tend to want to time it right. Because your DC has recurrent UTI, the NICE guideline recommends doing this scan.
MCUG is another sort of dye test. You can only do it on younger kids (mostly less than 2 years, after that it tends not to work very well). A catheter is put into the bladder, dye is put into the bladder, then pictures are taken as the child wees. The pictures show where the dye goes. What is meant to happen is that it all comes out the urethra (the tube to the outside). Sometimes some of the urine/dye shoots back up into the ureters (the tubes down from the kidneys), or even all the way to the kidneys. This is called reflux (or Vesico Ureteric Reflux). If a child has reflux, it shouldn't really make them more likely to have water infections (unless it's so bad that the urine isn't draining), but it means that if they get infections then it's more potentially serious, as they can head up to the kidneys. They also look to see that all the urine is draining out properly. NICE only recommends doing it if the child is under 6 months old. Some experts would still do it in any child under 2 years with proven wee infection, more would only do it if the DMSA scan showed any problem. I tend to do it if a child under 2 is still having lab-proven UTIs despite sorting out fluid intake/constipation/hygiene, even if the DMSA is normal. But, again, there is some radiation, so tend to want a good reason to do it.
MAG3 is another sort of dye test. You can only do it on kids who are able to wee on demand, so not usually preschoolers. The dye goes into their veins, but is processed a bit differently by the kidneys than the DMSA scan, so it looks at the urine flowing down from the kidneys to the bladder and out. But you can only get the pictures to show where the dye/urine goes if they can wee (on demand) at the right time after the dye is given. NICE doesn't really tend to recommend them in anyone. They tend to be used if the DMSA scan showed a problem in an older child, or if a child had reflux on the MCUG when they were younger, and you want to see if they've grown out of it.
Okay, that's the background. To come back to your specific question. In a child with previous problems with constipation, and milk intolerance (did they only ever mention lactose intolerance, as I wonder if it may actually have been the cows milk protein intolerance, as that can cause major constipation issues), and actual impaction, I would be very surprised if there was a structural problem from the gut to the waterworks causing an issue (although reflux problems are no more or less likely than usual). But I would want to ask a LOT of questions about whether the constipation was 100% sorted out, or whether it was just ticking along. because "just ticking along not really sorted" constipation makes waterworks infections a LOT more likely - so I'd be wanting daily non-straining pain-free passage of reasonable amounts of soft poo, and no poo to feel in his tummy. If they're having lots of water infections, then you tend to need perfection in managing their constipation (and fluid intake, and hygiene, and weeing pattern when well) in order to break the cycle.
Hope that helps. Sorry I went on so long. I'd better get back to what I'm meant to be doing...writing a presentation to teach a bunch of GPs about waterworks problems in kids! Timing!