Tepezcohuite/mimosa tenuiflora identification

[PP956K]

Hello everyone I did some AI identification on this tree I found at my dads house well he ain’t with us but every now and then I go to cut the yard clean etc he has a couple apartments he rented out and as I was talking to one of them I mentioned him that I’m wanting to plant a tepezcohuite at home or replant one he said your dad had a huge one in the back but he cut it down to stump a while back said it had purpleish color flowers and twigs went back there and the stump has a few new stems growing I took a couple pics. if anyone can help me verifying it’s mimosa and if I can remove with the root and replant it at home or what’s best leave it there. thanks in advance and appreciate everyone that has guided me here and all the info much love y’all

Oh and last three pics is an old eucalyptus tree bin that tall since I was a kid

 

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I don't see thorns, I don't think it's hostilis. Hostilis = hostile in latin.

 

[dreamer042]

1. Mesquite (Prosopis species)
Likely Velvet Mesquite (Prosopis velutina) or Honey Mesquite (Prosopis glandulosa)

2. Eucalyptus
Most likely a river red gum type or a closely related eucalyptus species.

 

[PP956K]

I don't see thorns, I don't think it's hostilis. Hostilis = hostile in latin.

Oh I didn’t know that thanks. well there’s some like that bark but with thorns there’s a couple here at my house let me post a pic of one but I’ve never seen it flower I always thought this was a mezquite

 

[PP956K]

This other one is similar up front of my house but has these seed pods no thorns also thought it was a mezquite as well