まちどおしい to express own "feeling" that time to wait for something is very long and wishing it comes soon. まちどおしい is written as "wait + far" まつ＋とおい so I think it is used when we express to wait for a long time comparatively. For example, "It is snowing and too cold! I can't wait for summer from now" I would use まちどおしい.
But also we use it like "I can't wait to see my boyfriend tomorrow", it sounds like even it is a short time but she must feel the time longer than the actual time.
まちきれない is written as "wait + cut (finish,end)" まつ＋きる” "cannot wait throughout/completely and make one's next move." For example, I have been waiting for my friend for an hour but she hasn't showed up yet. I cannot wait for her anymore so I go home. I would say まちきれない in this case.
Shifting from it, まちきれない is used as " cannot wait for something fun, itching to do it soon! "
まてない is just " action". the same as "cannot go", "cannot do" Can you wait for me 5 minutes? No, I cannot wait! I want to go to restroom right now!
For your question, "I can't wait for the trip this weekend" I asked my co-workers and they chose " まちきれない" , but I think まちどおしい is maybe OK if it is the beginning of the week when you set for.
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