What´s the difference between she´s got me spending and she´s got me to spend ?
This is a variant of the "What's the difference between the "verb-ing" form and the "to verb" form, which is probably the second most asked question on the site at the moment, so you might want to seek out some of those posts as well.
In this specific case, in which you've use the present perfect:
"She's got me spending every weekend with her" or
"She's got me spending a lot of money on her" both imply an ongoing situation.
"She's got me to spend a lot of money on her/time with her" does not necessarily mean that it's still happening.
However, there are a lot of idiomatic uses of "get" and "go", so don't expect "She got me going" to mean the same as "She got me to go".