Substituting instant imitation flavored pudding mix and cake mix in Bundt Cake recipe
Yes, you certainly can start from a similar recipe and adjust from there. I would not try to replicate instant pudding mix, though. If you don't want to use a store-bought pudding mix, I would suggest you replace that with a different filling entirely.

My preference is usually to go with a "scratch" recipe that I already like and adjust from there. For a dark chocolate cake with a white chocolate and raspberry filling, you have a lot of options, really.

Most bundt cake recipes make about 12 cups of batter. I think you want only 1 to 1 1/2 cups of white chocolate batter at the most. If you end up with more than 12c total, you will overflow a standard bundt pan, so you can either reduce the dark chocolate cake recipe or you can plan to make some cup cakes with the extra. :-) You'll want to fill your bundt pan to about 2/3-3/4 of the height of the pan depending on how much you expect the cake to rise. I'd expect a light and fluffy cake recipe to rise a lot, a pound cake to rise less. (if in doubt, 2/3 and/or put the bundt pan on a cookie sheet -- I usually put a cookie sheet under mine anyway to avoid a mess in the oven.)

Some filling options

Raspberry -


If you put jam as a filling directly in a cake or brownies, I find that it can tend to be soggy. I think sauce is going to be even runnier than jam. I'd recommend cooking that down (maybe with some cornstarch) to get it to a thicker consistency before using it as a filling. 
Alternatively, take a 1-2 cups of fresh or frozen raspberries and toss them in 1-2 T cornstarch and 1/4 - 1/2 c sugar and cook them on the stove until everything turns into a bubbly, thick sauce. (I don't know how much raspberry you want, but about 1 c berries : 1 T cornstarch : 1/4 c sugar)


You can also add a little bit of extra flour to the white-chocolate part of the filling to counteract some of the extra moisture from the jam/sauce, but if it seems really runny, I think you're going to end up with a soggy cake.

White chocolate -


white-chocolate flavored cream cheese filling (8 oz cream cheese, ~ 1/4 c flour, 1 egg, white chocolate chips or whatever you want to use for white chocolate flavoring -- I'm assuming there's enough sugar in the chips)
about 1 - 1 1/2c of batter from your your favorite white chocolate cake recipe + ~1 Tbs extra flour to counteract extra moisture in the raspberry sauce
play funny games with your favorite dark chocolate cake recipe to reserve out about 1/8th of the ingredients and add your white chocolate flavoring/chips to that portion (and about 1 Tbs extra flour)


When you assemble it, put about 1/2 - 2/3 of the dark batter in, then half the white chocolate batter, then the raspberry, then the rest of the white then the rest of the dark. 

This is sort of similar to what I'm picturing: 
http://famkitchen.blogspot.com/2015/06/chocolate-amaretto-cake.html