Go with your gut instinct.
That's all I have to say.
No sense risking things just to please a 13 year old... and why is he so so pushy about the 4 year olds coming over to play with him anyway? Most 13 year olds, have their own thing going and their own peers and activities....
NO SLEEPOVER. NO WAY. That is what I say.
You do NOT LET A 13 YEAR OLD DICTATE your parenting or your gut instinct or your rules, for your own family.
Thankfully, your Husband backs you up and sees this too.
Do not let your kids, be unsupervised with this teenager.
If you are present when this 13 year old is being so physical/touchy with your 4 year olds.... then you simply say "don't do that, it is not appropriate..."
There is a BIG difference, between a 4 year old and a 13 year old.... but this does not seem like normal behavior.
I once saw a show on a teenager boy, who with his little 2 year old sister... would be like that too her... wrestle with her/hug/kiss and be real "touchy." But, the parents videoed him once because they were suspicious... but in the video play-back... it could be seen that amongst the "wresting"... this boy was actually putting his hand on her genital areas. Not by accident. It was purposeful. Intended. This boy... even though he was a teenager... was "molesting" his little sister. Which is what the parents suspected. A rude awakening.
The Host of the show and an expert... said that this is often the way predators/molesters behave... being touchy with the child, affectionate... but it just gets the "child-victim" desensitized to being "touched" in certain private places. It is gradual. Then over time... more demonstrative things occurs.
Not saying this is what that 13 year old is doing.... but go with your gut instinct. Mom's have an extra radar...
Also, I would wonder how this 13 year old is with his own siblings???
Next, if he is an uber affectionate teenager... then he would be this way with everyone across the board... not ONLY "specifically" with the 4 year olds.
All the best,
Susan