Could be Vinca minor, could be Trachelospermum jasminoides but the shots are too distant to id it confidently. A geographical location would also be helpful. As for the snake, it could hide in any planting and do you know it was a dangerous species?

Baton Rouge, Louisiana. I will try and get a better picture also

Of the two leaves look most like the star jasmine. In LA poisonous spiders and probably chiggers and ticks are possible in addition to poisonous snakes, anywhere in the yard - with or without low carpeting shrubs being present. In fact after a couple I know looked at a bulldozed bare building lot in VA one time the female half turned out to have picked up chiggers there.

After the two ending up buying an existing house and garden near Tampa Bay it turned out there were small disease spreading biting flies prevalent in the area. And he felt it necessary to go out and spray the whole place with insecticide because of this. Even though his background was in environmental science.

Point being removing that otherwise nice patch of ground cover is not going to assure your child of a 100% hazard free play area, where no attention needs to be paid to possible pitfalls.

That’s 100% true. I also was going to build a deck where it’s located also

Might be able to get it to come loose and pull up adequately with a mattock.

looks like wintercreeper euonymous to me. commonly used in this area exactly as pictured. you can mow or trim it down to a very low height for an attractive ground cover.

I do not believe it to be Euonymus fortunei. The leaves are the wrong shape and the wrong texture. Too acutely pointed and too thin.

Yes.