I'm sorry but I'm totally confused by this whole thing

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I think that you want a pup but only will see it part time is somewhat jumping the gun and the responsible thing would be to wait. It might all sound hunky dory now but I'm guessing it won't be so great after the pup barks all night or pees all over and someone else has to take care of it because you had to have a pup RIGHT NOW! I'm sorry but I see something like this breaking up a relationship or at the least making things strained between either you and the boyfriend or you and the BF's parents who's home it is.
You also said something about vet visits were covered for 4 months. Well I'm thinking the man's intentions with agreeing to this meant sick visits but I am reading from your post that you are thinking ALL visits. The vet will need follow up well visits and shots during the next 4 months and $18 a shot is only for the shot and an exam fee is usually customary unless somebody knows something I don't know!!!!
I'm sorry but it reminds me of when my kids see someting on TV and just HAVE to have it. They go nuts for the commercials and nuts in the stores but EVERYTIME I go ahead and get it, it wears off and then the toy is forgoton or disgarded.