The most likely reason that you don't "get" space... is because you do not WANT space...

Think about that friend you have... that you kinda like... but that can be REEAAAALLLL annoying to be with for any length of time...

It's kinda like that... but different...

Yes... yes... it has been discussed before... and it will be debated again... many times into the future...

If the LBS gives space in a way that they THINK the WAS wants space, will that not indicate they do not care and make it easier for the WAS to move on...

Try to imagine it this way:

+ keep smothering her and she will want to leave in a more permanent way... and probably resent you...

+ give her space and she might want to move on... but at least she won't resent you so perhaps the two of you can get back to being better friends and co-parenting...

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the alternative is:

+ give her space and she might actually miss you... or at least have enough time to not dislike you... helping her consider that perhaps there might be an opportunity to try... one more time... to work things out...