Polyurethane finish over stained wood - can I combine brush and rub on techniques?
I wouldn't recommend using a bristle brush at all. Use either a foam brush or a lambskin applicator. I don't really see a reason to switch between the two, but it should be ok.  Make sure you follow the manufacturers recommendations.  You do not want to begin sanding until the solvents have evaporated and it begins curing.  Also, time between coats has an upper limit.  See the manufacturers website.

Two additional thoughts:

You can use a thinner such as mineral spirits to thin out the polyurethane.  You will need more coats, but it will help eliminate stroke marks.

If you really think a small application like a coffee table will take that much abuse, you could use "Glaze coat". It is a two part that goes on extremely thick and works very well.  Commercial bar tops and table tops often use it. It's not cheap.  Last time I used it I paid $25 for 9SF of coverage, but it goes on smooth and when you are done you could practically weld on it ("slight exaggeration")