I have an exterior stucco wall that's not in super great condition. The outermost-layer was applied very badly and is flaking off, so doing a patch job or yet another layer seems like a bad idea because the layer it would be adhering to is itself not adhering well. As part of this project, I will be adding rigid foam insulation to the exterior side of the wall. My question is this: can I reasonably screw-and-glue the rigid panels right over the existing stucco cladding, or should I really remove all the prior layers of stucco first and attach the foam directly to the wall sheathing? Advantages and disadvantages to each?
Fastening rigid board by screwing through the stucco into the cladding (or framing) will hold the stucco in place, so its poor condition matters little. Remove any mold or rotted stucco, and remove any organic debris. I wouldn't bother trying to glue to flaking stucco.
Additionally, the stucco left in place will continue to provide a moisture, thermal, critter, and sound barrier that is desirable.
Advantages: cheaper, cleaner work, and easier to do.
Disadvantages: the exterior will be slightly (1/2 inch?) larger.
The only advantage I can think of to removing the stucco is the idea that you'll remember it as getting rid of the mess.
I thought I remembered that you had asked questions about other portions of work related to your house. I checked back to it and seen you are prepared to do anything that is going to give the best result, with good reason. Shortcuts can work, and may even give the same look, but if you are going to go through a major renovation, a shortcut can cost in the long run if you plan to keep your home for years. Because of what you propose to do, if done incorrectly can cause your home to degrade before its time. My answer will tie in a bit to the question you asked about sequence of work. It may repeat some things, it may elaborate on some. I hope it will wrap it all up for a supreme product, and with the help of others comments, even pick up on some extra good advice.
First I would remove all the stucco, leaving the windows intact, since the stucco only meets the window trim and will be easy to salvage the windows integrity for now. This will give you an opportunity to inspect all the sheathing, and with that the framing too. I will hazard a guess that the sheathing is a diagonally laid 1X6 or something similar. If the sheathing has major issues, it is easy to repair at this point and when you remove the sheathing to repair it, it will then be obvious if the framing is affected as well.. then of course a call will need to be made how to approach those repairs too. As in cut sheathing, sister studs or ?? then replace the removed sheathing with plywood, just in the repair area.
Next is to decide what type of weatherproofing you will choose to place over the now bare wood subsiding and foundation prior to adding the insulation a few steps down the line. If you go with a layer of exterior insulation over the foundation as mentioned in a prior question, I would use a liquid applied waterproofing membrane (LAWM) on the foundation walls and brought up onto the wood to seal the foundation to the wood above. Backer rod and other compatible sealants may be needed in conjunction with the LAWM, with the rest of the package I will detail, wood boring insects will have a hard time getting to the wood. A word of economics, this stuff (LAWM) cost about 3 times the amount of house wraps. If you simply place the foam on the foundation wall, termites and such will have a protected haven to travel to your framing. The Tremco (no, I do not work for them nor am I a paid endorser) line of products is what the company I worked for applied to accomplish this. The thinset used to bond the foam to the wall for the EIFS system should stick to it and grab. A test spot would confirm.
Once the foam is on the foundation and the waterproofing under it, the waterproofing should extend 4" or so above the foam to tie in the first piece of through-wall flashing. Copper is best, ZT alloy is better, do not use galvanized metal, and I would question if even a PVC coated heavy aluminum would not corrode with the layer of modified cement that is used in the EIFS system. Whatever metal is used the upper leg that mounts to the wall should be no taller than 3" so it can be tied into the lower level of waterproofing and insuring crawling bugs can go no further. Above this flashing, but lapping over the 3" leg applied to the building, you can use a house wrap of your choice. Although I would still use a liquid applied membrane approved for use above grade. This material is different than what is used on the foundation wall. Both products seal around nails that go through the membrane, but do not pull the nails out if one is driven badly. The material seals around the nail shank, but will not seal the hole after the nail is pulled. This will have your walls dried in after this phase.
Next will be the window replacement. Pull your old windows after the ROs if needed, repair the last bit of framing that the windows concealed. Add 2X2s at the sides and head of each opening if you plan to have nail fins or brick molding around the windows. If the windows will have a nail fin at the bottom, add a 2X2 there also. Omit if there is no brick mold there. Finish detailing the house wrap into the window openings before the 2X2s are applied. Add 2X2s before you touch up the LAWM, and coat the RO and 2X2s with the LAWM. If you use house wrap, install a plastic pan made for window ROs and tie it in with roofing nails with the heads overlapping the plastic flanges on the side and tie in with approved tape. What will be the drip edge of the plastic pan will be over the house wrap, so when the windows do leak, which they will in time, the framing is protected. If you use LAWM you will not need a pan, but I would set an angled sill (7 degrees+/-) so what water gets in, readily goes out. Set your new windows, do not use replacements, if you do there will be a break in your weather envelope, since these type of windows install in existing jambs.
Next flash your windows and doors with the same material used at the watertable (top of foundation). As a mention, this foundation flashing is bent so it is out far enough to allow the finish to go under its drip edge, about 3/8" past the foam will do here. This will not need to be done at the windows, just the foundation. If using house wrap, flash the sides of the windows to protect the 2X2s from moisture. This can be done before the windows are set also. Then set the top flashing last. I usually run the head flashing 1/4" past the sides of the window to protect the caulk joint at the top. When I caulk the sides, I start under that small extension of the flashing: that way rain water will not get behind the siding from the top. The flashing is not set flat either, I do not bend my flashing at a 90 degree bend, more like 80 and press it in so the flashing flexes down tightly at the outside corner of the window trim and angles up to meet the subsiding. This creates a positive fall so weather will not run back to the framing, and I do not caulk the top, caulk will hold in water as well as keep it out. I got a little ahead of myself in some places, but after the flashing is set, install the upper run of foam, nailed in place if you like and add the stucco finish.
Depending what type of trim you use around the windows, for example, if you use a 5/4 material or brick mold, you can add 2" of foam, get real good R value, and still have a nice trim detail exposed beyond the stucco. Maybe even trim the windows with EIFS.
Just my 2 cents worth.