Is there any possible way to change the cabinet door without buying new doors..honestly anything is better than what I have right now as in the cabinet door itself. Any input is appreciated. My dad worked in construction and my husband thinks he can change these to shaker cabinets...

I understand what you're saying. You are basically adhering false fronts to the panel as if you were putting a mat around a picture before framing it. It will be an overlay. I did a similar thing in reverse, I cut thin panels of wood to set inside a very deeply raised frame cabinet door to hide odd wood carvings. I then painted the entire cabinet door and it looked fine. Lived with it for 15 years until I could afford my dream kitchen two years ago. The thing I think you should be mindful of is if the addition of another layer of wood will impact the door's ability to open. How is it hinged? If the door were 1/4 inch thicker, would it swing open or would it smack up against the cabinet frame and not open? Worst case, get a piece of 1/4 inch melamine https://www.menards.com/main/building-materials/panel-products/prefinished-panels/dakota-trade-1-4-x-49-x-97-melamine-panel/mel1449pbwhite/p-1444428246997.htm or smooth plywood of some kind such as this https://www.lowes.com/pd/1-4-in-Lauan-Plywood-Application-as-2-x-4/1000068895?cm_mmc=shp--c--prd--lbm--google--lia--211--precutplywood--1000068895-_-0&store_code=444&placeholder=null&gclid=Cj0KCQiAtOjyBRC0ARIsAIpJyGNTv1u9rLn_8PDUq7eouNQ8v5GxwvbH5w0AKWy84QZcA6oXBXv3qDAaAi3dEALw_wcB&gclsrc=aw.ds

and try one. Or, adhere a strip of 1/4 or 1/8 inch wood of any kind to the front edge of the cabinet on the hinged side and see if the door will still open.

Sometimes we gotta live with what we've got until we can change it out, so I say, try a sample and see what happens. If it works on the cabinets, I wouldn't even do the drawers, simply change the hardware on them to tie it in with the cabinets. Or do all the cabinets and see if you need to do the drawers.

So far we have this...1/4 inch are the boards on the side.. that’s what I’m worried about is the swinging cabinet door isn’t going to open all the way. My husband thinks it will 🙄. We have European hinges on the cabinets.

I made a small cabinet door by using a plywood slab and adding thin trim, as you are planning to do, but--it was made for a new filler cabinet at the end of a run of vintage cabinets with exposed hinges. I used exposed hinges to match (m/l) the existing hinges--don't have any idea if European hinges will work.

ETA, here's a pic taken just after the door was installed. I think it matches the old cabinets enough that most folks think it's always been there:

One solution if it doesn't have enough clearance to swing out would be to create a small notch in the overlay that creates enough room to clear the hinge so the door can open. I think the one @mama goose_gw zn6OH made looks great. I would test out one on the flat panel cabinet and see how it looks. Worst case, you take it off and you've had a fun afternoon working the project. But IMO, European hinges make it workable.